I often hear it said that Luke got his history wrong in Luke 2:1-6. He refers to "the first census that took place while Quirinius was governor of Syria". It is said that there was no such census; it never took place.
This is a serious charge to levy against a gospel writer who is historically impeccable when he records any fact for which we have independent records, and who says (Luke 1:1-4) that he worked hard to check everything out with primary eye witnesses.
Much ink has been spilled on this. However, the commentary on Luke by Darrell Bock is thorough and contains a helpful excursus examining this question at length. For my own future reference, and for the benefit of others, here's a summary of his argument.