I have in mind in particular two main issues (though there are certainly many other issues we need to work on as well): 1. The relationship between Christianity and the civil magistrate. 2. The unity of the church. I used to think of these two issues as basically unrelated, but I have come to see that they are intimately bound up with one another.
CHRISTIANITY AND CIVIL GOVERNMENT
The historic position of the Christian church on the relationship of Christianity to civil government, held almost unanimously (except for the Anabaptists and perhaps a few others) up until the past couple of hundred years, is called the Establishment Principle. The Establishment Principle holds that civil authority, just like all other delegated authority, comes from God and therefore is accountable to God and his law. Civil magistrates are ministers of God, as Paul puts it in Romans 13. They have authority from God to fulfill particular functions--namely, using the power of the sword (laws and lawmaking) to preserve a public sphere where good is encouraged and protected and evil is discouraged and punished. They are to look to God's law to define good and evil and to gain the wisdom to carry out their functions. Societies are to have Christianity established as the officially endorsed religion. And beyond that, the state is to formally recognize the true de jure church of Christ as the one established church. It is to recognize the ecclesiastical authority of church courts and officers of the true church, and it is to use its power for the protection of the peace and purity of the church so far as this falls under its legitimate jurisdiction.
Over the past few centuries, however, much of the Christian church has lost sight of this principle--to varying degrees. It started with the toleration of schism and heresy in the 1600s. This was directly influenced by a view called voluntaryism, which has become very popular in the church. Voluntaryism holds that the church is not to be established and supported by the state but instead is to be left alone as a voluntary organization to fend for itself without formal recognition--as if it were nothing more than a country club. The weaker forms of voluntaryism might agree that the civil magistrate ought to be generally Christian and follow basic biblical principles in governing, but it would hold that the state ought to be tolerant of the various differing denominations within a broad "orthodox Christianity" and not establish one of them as the only established church. The strongest form of voluntaryism would say that the civil magistrate should not even endorse Christianity broadly speaking. It should be secular--which is taken to mean that it should be neutral between all religions. In effect, this form of voluntaryism teaches that the civil government should reject the Christian worldview in favor of the establishment of an Agnostic worldview.
To get a glimpse of the two differing views, compare these two quotations, one from the original Westminster Confession of the 1640s and the other from the revised American edition of the Westminster Confession of the 1780s:
The civil magistrate may not assume to himself the administration of the Word and sacraments, or the power of the keys of the kingdom of heaven: yet he hath authority, and it is his duty, to take order, that unity and peace be preserved in the Church, that the truth of God be kept pure and entire; that all blasphemies and heresies be suppressed; all corruptions and abuses in worship and discipline prevented or reformed; and all the ordinances of God duly settled, administered, and observed. For the better effecting whereof, he hath power to call synods, to be present at them, and to provide that whatsoever is transacted in them be according to the mind of God (Westminster Confession 23:3 as approved by the Church of Scotland in 1647).
Civil magistrates may not assume to themselves the administration of the Word and sacraments; or the power of the keys of the kingdom of heaven; or, in the least, interfere in matters of faith. Yet, as nursing fathers, it is the duty of civil magistrates to protect the church of our common Lord, without giving the preference to any denomination of Christians above the rest, in such a manner that all ecclesiastical persons whatever shall enjoy the full, free, and unquestioned liberty of discharging every part of their sacred functions, without violence or danger. And, as Jesus Christ hath appointed a regular government and discipline in his church, no law of any commonwealth should interfere with, let, or hinder, the due exercise thereof, among the voluntary members of any denomination of Christians, according to their own profession and belief. It is the duty of civil magistrates to protect the person and good name of all their people, in such an effectual manner as that no person be suffered, either upon pretense of religion or of infidelity, to offer any indignity, violence, abuse, or injury to any other person whatsoever: and to take order, that all religious and ecclesiastical assemblies be held without molestation or disturbance (Westminster Confession 23:3 as revised by American Presbyterian synods in 1788).
In the original version, there is only one church, and it is to be formally recognized and protected by the civil magistrate. In the revised version, we have multiple denominations of churches which are all to be protected by the civil magistrate without any of them being established above the others. (There were other changes made in the American versions of the Westminster Documents as well over the years, such as the deletion of the phrase "tolerating a false religion" under the list of sins forbidden in the Second Commandment in the Larger Catechism. See here for more details on these differences.) Although the revised Confession focuses its attention on different denominations of Christians rather than various groups of religionists in general, it evinces a laissez-faire attitude towards truth and a tolerant attitude towards error that is, I think, on the way towards a broader acceptance of diversity and non-establishment (and I am confirmed in that sense by the deletion from the Larger Catechism just mentioned).
THE UNITY OF THE CHURCH
The historic position of the Christian church up until the past few centuries is that there is only one church of Jesus Christ and that the oneness of the church is to be recognized by all the churches being in formal communion under binding councils throughout the world. Whenever there were splits between different Christian groups, both sides claimed the true legitimacy of being the de jure catholic church and accused the other side of being illegitimate and schismatic. The idea that there might be multiple independent churches side by side which are all legitimate was unthinkable. This idea of the unity of the catholic church is upheld both in an episcopal and in a presbyterian view of church government.
However, starting especially in the 1600s, a new view began to grow in prominence and is now, to a great extent, a dominant view among Christians, even affecting the views of those who still call themselves presbyterians, and that view is congregationalism or independency. In the congregationalist view, the church need not be in formal communion beyond the local congregation, and the highest church court is the local congregational leaders. This view is widespread in the evangelical world today, and a partial version of it mixed with some aspects of presbyterianism is dominant in the Reformed world. In a congregationalist or semi-congregationalist view, there is not only one de jure true church, but there are multiple true de jure churches existing in multiple independent denominations.
THE TWO ISSUES ARE RELATED
Hopefully you can see from what has already been said that these two issues are closely related to each other. Look back again at the two quotations from the two versions of the Westminster Confession. Again, in the original version, there is only one church which is established by the civil government. In the revised version, the church consists of multiple independent denominations which are all treated equally by the civil government. The revised version of the Confession embraces a semi-congregationalist, denominationalist view of the nature of the church.
The move from the Establishment Principle to voluntaryism is closely related to the move from presbyterianism to congregationalism or semi-congregationalism. If the courts and officers of the church are formally recognized and their legitimacy is acknowledged by the state, this naturally tends towards the unity of the church. The officers and courts that are recognized by the state will naturally recognize each other, and thus will tend to be in formal unity and accountable to each other. Those professing officers and courts that are not recognized by the state will naturally be seen by everyone as being illegitimate. So there will be a tendency to see the church as one.
On the other hand, when the state disestablishes the church and treats it as if it were a voluntary country club, this encourages the people of the society to look at the church in the same way. Instead of asking, "Which church has legitimate authority?", the question will tend to be, "Which of these voluntary church organizations on the market do I like the best so that I would like to be united to it?" And this state of affairs, of course, encourages multiple different churches to arise which are not in formal communion with each other. After all, what's the problem with having multiple country clubs? The more the better, as it allows more options to suit diverse tastes. So a situation of state disestablishment will tend to cause fragmentation and congregationalism or at least semi-congregationalism in the church.
And the reverse is true as well. If the church has a sufficient concern for its own unity and authority and the truth it proclaims to avoid denominationalist sorts of attitudes, then if the civil government wants to embrace Christianity, it must take the church along with it. And the church's concern for truth can impact the larger society in that direction as well. But if the church develops a laissez-faire attitude towards truth and allows itself to become fragmented, this will encourage the state to care less about truth itself (which will be likely to tend eventually towards something like an Agnostic secularism). Also, the state will be unable to establish any one church (because the church itself has given up on the concept of formal church unity) and so will end up adopting a voluntaryist attitude towards the multiple denominations that exist.
IT IS TIME FOR CHANGE
The natural twin ideas of voluntaryism and congregationalism/denominationalism have become so entrenched in the thinking of the church today, even among the Reformed churches, that it is going to require an immense amount of swimming against the current to change things. This is why I use the language of reformation. Of course, any change for the better is a reformation. But there come times when error becomes so entrenched that an entire movement is needed, a movement full of people who understand what needs to be done and who are willing to run uphill against the strong negative opinions of their peers and even their superiors in order to do it. Think of Martin Luther. By his time, the errors of popery, through hundreds of years of slow growth, had become so entrenched in the western church that no quiet, meek (in the colloquial sense of that term) sort of persuasion was going to be able to effect change. There were plenty of people who were aware to some degree or another of the problems and had some vague sense that it would be good to fix them, but were not willing to be radical enough to do anything about it. They preferred to send the problems to committee so that the proper channels--the official church and civil courts, the academic community, etc.--could deal with them. The problem is that when errors are entrenched to the degree they were at that time, this method simply isn't going to work. The committees will simply spend ages discussing the problems, wishing something could be done, but they will not tend to develop the momentum necessary to overcome the inertia of familiar errors. There will be endless discussion, but no change. If change is to happen, it will take people who are willing to be bold enough to say, "We simply cannot tolerate this any longer! We are going to do what is right and effect change, even if it means we have to act in ways that may incur (to put it mildly) the disapproval of our more conservative peers and leaders." Martin Luther, of course, was such a person, as were the other reformers. Many of those sympathetic to some of the concerns of the reformers nevertheless opposed the radicalism of the Reformation. They counseled the reformers, "Slow down, take a deep breath. Yes, there are problems. But don't keep pushing so hard and rocking the boat or you will cause more problems than you will solve. Just respectfully attempt to bring up your concerns (at least those that won't make people too mad at you) in the proper committees and let the civil and church leaders deal with it." The reformers' response was, "No, we must now begin doing what needs to be done. Our leaders have too much to lose and they are too comfortable. If we wait for them to change things, things will never change. God has called us to do what is right, even when the rest of the people of God refuse to go along. We will not wait to do what is right until we have the approval of the corrupt present institutions." This response did not reflect a "taking matters into their own hand" sort of attitude and a failure to rely on the grace and providence of God. The reformers were quite conscious of their need for God's grace and power to accomplish anything. But they also knew that God had given them duties to fulfill, and they had better be about fulfilling them whether it rocked the boat or not.
I don't think our present situation is as dire as it was in the sixteenth century. But, like in those days, on the two issues I've been discussing we face a community of churches and nations who have become so entrenched in certain ways of thinking and doing things that it is going to take people who have the boldness of reformers and who are willing to endure the tide of criticism that will come to them, and the accusations of "radicalism" that will be hurled their way, in order to attempt to do what they are supposed to do to promote the reform of both church and state in these areas. We need to advocate for truths about civil law and government, religion and politics, human rights, etc., that are immensely unpopular and will subject us to ridicule and hatred. We need to advocate for truths about church unity and authority--such as forcing people to confront the question of de jure legitimacy in the church and attacking denominationalist attitudes, and even acting on consistent biblical principles in our own practical choices regarding church affiliation--that will bring upon us the ire of those who have grown accustomed to the status quo and despise rocking the boat in this area too "radically." (And we need also, on the other hand, to have the wisdom to know how to temper radicalism and not allow it to go beyond what is appropriate and lawful, recognizing that we must seek for peace and order as well as purity and change.) Let us have the courage through our faith in God's providence and grace, and enough respect for the authority of God who commands us to do our duty no matter the opposition we meet, to wake up from the slumber that we've all tended to fall into on these issues, do what we personally need to do, and call others to do likewise. By God's grace, it worked in the sixteenth century! And I don't think God has gotten any weaker over the past few hundred years.
See here for more on Christianity and civil government (and an invitation to join the Reformation Party), and see here for more on presbyterianism and church unity.