Here's an excerpt:
*There was no census of "all the world" (read: the entire Roman Empire) declared by Augustus; at least, if there were, it's not mentioned in any Roman documents that we've uncovered so far. The census was of Judea, Samaria, and Idumaea--not Galilee (where Luke puts Joseph and Mary). Quirinius used the opportunity to also conduct a census of Syria.
*The notion that each male would have to register in the home town of a remote ancestor is unbelievable. The entire Roman world would have been turned upside-down. There would surely have been records of such widespread dislocations, and there are none. Augustus was arguably the most rational of the emperors, and would never have ordered such an irrational thing.
*Ancient census-takers wanted landowners to be connected to their land, for tax purposes. The census-takers traveled, not those being taxed.