A former professor at IWU used to say that some of the commands of Scripture were for "one time" (go sell everything you have), some were for "that time" (women veil your heads), and some were for "all time" (love your neighbor). This way of sorting out how to apply the Bible to today will probably stick in your head long before anything else I have to say in this post.
The problem is of course sorting out what is what. Although many Christians think they apply everything in the Bible directly to themselves, even the Amish do not go and sell all they have and give to the poor. Most of us don't greet our brothers with a holy kiss. Most of us don't stone disobedient children. Whether we will admit it to ourselves or not, all of us are selective (appropriately) in what we apply from Scripture--we just may or may not be consistent in how we select.
A starting point is to recognize that almost everything in Scripture--if not everything--was at least "that time." The question is not whether a text in the Bible was for "that time" or "our time." The question is whether it was just for that time or for that time and our time. Even the prophesies of Scripture were primarily for the people in front of the prophet and only secondarily to us. There may be exceptions, but they are exactly that--exceptions.
For this reason, it is very important for us to focus on the "all time" principles of Scripture. For example, Jesus and pretty much everyone else in the New Testament boiled down all moral requirements to "Love God and love neighbor." Any specific statement in Scripture that you might be tempted to use in a way contradictory to this love command is not "all time," and these two commands themselves can never contradict each other if understood correctly.
Let me give you another example that gets closer to the chase. In the years leading up to the Civil War, many Christians argued from the Bible that abolition was not biblical. Does not Paul tell slaves in 1 Corinthians 7:21 not to worry about being a slave? Does not 1 Peter 2 encourage slaves treated unjustly that they are being like Christ when they suffer under it? Does not Colossians 3:22 tell slaves to obey their masters?
By contrast, those who argued for abolition argued not so much from the specific "that time" commands of Scripture but from the bigger principles. If in Christ there is neither slave nor free, then wouldn't a world in which slavery is abolished be more like the kingdom than one with it? And why would we want to wait until the kingdom if we could move in that direction now? What would a master who truly loved a slave as him or herself do?
You won't be surprised to know that I believe the issue of women in the church and the home is playing out a similar dynamic today, where those who focus on one verse in particular are missing the bigger picture of what the kingdom will be like in regard to men and women. But that is not my point. My point is that the authority of Scripture is invested in the whole canon and in the broad principles of the whole more than in any one individual verse.
Every individual verse contributes to that whole, but we are prone to mistake the "that time" for the "all time" if we don't process the individual verses in the light of the rest. In fact, it would be interesting to see if the more detailed we get with the biblical text, the more likely we are to get into "that time" territory. Evangelicals have developed a complex process for moving from that time to this time in general. It involves figuring out the points of continuity and discontinuity between the specific original context of a text and our context today. This is not only a task that begs for great expertise but it is a spiritual task that Christians should do together more than as lone ranger believers.
It also seems common for individuals to read a text more "spiritually" when we get down to individual verses and texts. God might make a verse come alive in a way the biblical author never intended and tell you to move to Florida. It would be hard to deny that the Spirit speaks this way regularly. The problem is knowing for sure when it is the Spirit and not something else. Impressions beg for confirmation from fellow Christians, from spiritual common sense, from long-standing Christian understandings, and of course from the other parts of Scripture.
So always be open to the Spirit speaking to you directly through a verse. Be ready to work hard together in the application of individual passages today. But always look for the "all time" in the text, the big principles. It is ironic on the deepest levels that some use the Bible as a tool for evil. The Ku Klux Klan comes to mind, whose membership was filled with good church going people and even pastors.
The cure is the "all time" of Scripture. Seek it, learn how to know it, and always submit to its authority!