Here is a list of eleven fairly clear insights that have not fully trickled down to the popular level. Nos 1 -10 were written by Ken Schenck (Dean of Wesley Seminary at Indiana Wesleyan University and Professor of New Testament and Christian Ministry) and no 11 was contributed by a former colleague Revd Eric Potts.
The list is not exhaustive and there will probably be others that could be added :
1. The Jews were not trying to earn their salvation by good works.
2. The apostle Paul did not struggle with a guilty conscience, either before or after he believed in Jesus as Christ.
3. St Paul saw works as an element in final salvation. What he did not believe were required for justification were "works of Law," especially those aspects of the Law that separated Jew from Gentile (e.g., circumcision).
4. The letter to the Romans is not primarily about how to get saved but about how the Gentiles can be included alongside the Jews in the people of God.
5. The Law that is referred to in the letter to the Romans is the Jewish Law, not some abstract moral law.
6. Paul did not change religions when he believed on Christ. He probably changed Jewish sects. All the early Christians saw themselves as Jews. The Gentile converts saw themselves as converting to a form of Judaism. It would be more accurate to speak of Christian Jews than of Jewish Christians in the earliest church.
7. The Pharisees were all strict but they were not all legalistic in the sense of only caring about rules for their own sake. Jesus puts them in the "healthy" and "righteous" category, at least initially, in several parables. Some of them became believers without leaving Pharisaism.
8. New Testament theology is theo-centric (God the Father centred) rather than Christocentric (centred on Christ).
9. The best approach to understanding the historical Jesus locates him within first century Judaism on a trajectory to the early church.
10. The earliest Christians did not see ethnic Israel as replaced but in a temporary state of unbelief.
11. The expectation of an imminent Messiah was held only by a limited number of Jewish groups, not by everybody; though it would not be surprising if some version of the idea was found in popular religious thinking. The idea that everybody expected a militaristic Messiah, is false.