There is a fantastic, thorough study of the Nativity story here:
http://www.infidels.org/library/modern/richard_carrier/quirinius.html
It goes into a lot of detail.
Short version: It really is a smoking gun that the gospel writers were making stuff up. The date of the census mentioned in luke conflicts with matthews account which places the nativity during the reign of Herod.
Prophecy declared that the messiah should be born in Bethlehem. Everyone knew that Jesus was from Nazareth. The two gospel writers attempt to deal with this in two ways. In Matthew's account it appears that Jesus' family lived in Bethlehem and had to flee to Egypt because of the Massacre of the innocents - when they returned they settled in Nazareth. Luke has the family based in Nazareth, they go to Bethlehem for the birth, and return to Nazareth. The two writers deal with the problem in two different and conflicting ways and are caught with the pants down.
Christian apologists have attempted to get around this problem in various ways, all of which are dealt with in the above link.