My thoughts are on the Jerusalem Council since my class and RECRS is shifting into this discussion soon. I have never been satisfied with the way in which scholars have handled this Council, because I haven't seen a proposal that fits all the evidence. I especially don't like "it never happened" because this position does not take into account all the evidence. But it also couldn't have happened as Luke says it did because it doesn't fit with what we know about things from Paul's letters.
1. The solution that Acts 15 never happened doesn't make sense of the fact that Luke knows about a decision (letter?) from James that resorts to Noahide laws, nor that these laws appear to have been known and observed by Christians as late as the third century. These laws have to have been instituted or invoked by someone somewhere in the first century in order to deal with the Gentile problem.
2. Paul's understanding of his meeting in Jerusalem recorded in Galatians 2 does not correspond to Acts 15, neither in terms of outcome or in terms of who was there and what was discussed. Trying to harmonize them results in apology, not history.
3. If the decision of Acts 15 had been made prior to the Antiochean Affair, it doesn't make sense that the apostles would then begin a counter-mission to Paul after the Affair and demand circumcision of the Gentiles in the churches Paul missionizes. It is very clear to me that the opponents to Paul are not unknown folks, but authoritative missionaries (even disciples) from Jerusalem.
4. Then there is that strange passage in Acts 21:25 that appears to suggest a letter having been sent out without Paul's knowledge about a decision made by James in terms of the Noahide laws, a decision that looks to be a compromise between Paul's radical position, and that of the Jerusalem Church, although no mention is made of circumcision.
5. Other observations?
So here is another thought experiment for you. How can the Jerusalem Council best be explained given the evidence we have?