The Census of Quirinius has always been my favorite argument against the historical accuracy of the Christian bible.
In the book of Luke (2: 1-7) it is described that around the birth of myth deity-man Jesus, Caesar Augustus decreed that the whole world would be registered (meaning his Roman Empire, of course). It is said that the first registration was taken while Publius Sulpicius Quirinius was governor of Syria. It then tells us that all went to their own towns, this could mean home towns or birth towns or ancestors towns (it is still debated on over the meaning).
So Joseph, being a descendant of David (we are told this, at least), went from Nazareth in Galilee to Judea, to a city called Bethlehem.
The problem of the town lies in the author telling us Josephs ancestry and because of his ancestry he had to leave his home town and travel to Bethlehem in Judea.
The above tells us, and rather plainly, that this tax involved the individuals ancestry and where they were registered.
Moving on.
You will notice that I underlined the word "first" when saying this was the first registration and that it was taken by Quirinius. I did this because there are records of 3 major census' being taken during the reign of Augustus, 28 B.C.E, 8 B.C.E, and C.E. 14. So, the very first census would have to be in 28 B.C.E or earlier.The earliest such provincial census was taken in Gaul in 27 B.C.E, the imposition of the census provoked disturbances and resistance. Keep that in mind.
Josephus records that a census was taken at that time, in Syria, around 6 or 7 C.E. after the exile of Herod the Greats successor Herod Archelaus. From this we can safely place the birth of the myth deity-man Jesus at around 6 or 7 C.E. (for those who do not know the Before Common Era and Common Era acronyms, that would be 6 or 7 A.D). I will let that sink in.
Now if Luke is true, then this places the book of Matthew in a difficult spot for it places the birth of the myth deity-man Jesus at the time of Herod the Great (2: 16-18), who died in 4 B.C.E, ten years earlier. The verses in Matthew tell of Herod the Great issuing a massacre of the innocents, a rather famous event that most likely did not happen. I will get into that n another post.
Back the the census.
In addition to all this, no other sources mention a Roman-wide census of this type (to include all peoples); the censuses carried out by Augustus were of Roman citizens only, not every person living in the region.
Most modern scholars agree that this is an error on the part of the author of the Luke, concluding that he created a literary fiction in order to place the birth of the myth deity-man Jesus in Bethlehem, unaware or indifferent to the chronological difficulty it presents.
The excuses given by those who will always give them are as follows:
1. An earlier census was carried out, or begun, during the reign of King Herod the Great.
The above could have happened but it still does not answer the problems of Quirinius, who is mentioned by name, being governor of Syria and carrying out the census. Quirinius was not governor of Syria until after the banishment of Herod Archelaus in 6 C.E. The two were never in power at the same time (Quirinius was governor of other ares, such as Crete and Cyrene in 14 B.C.E. In 12 B.C.E he was named consul of Rome and in 6 B.C.E. h was sent to govern Pamphylia-Galatia. After Pamphylia-Galatia he served as a chief adviser to Augustus' grandson Gaius Caesar, until he died from wounds suffered on a campaign.
2. That Josephus must be mistaken.
I find this ridiculous!  If he is mistaken on a simple matter of governorship  then all his works would be thrown into question. This would also create more problems for Christians for they use Josephus as the main source to the historicity of the myth deity-man Jesus.
3. The texts were mistranslated.
If this is true then how can you be certain that the rest of the Christian bible is true and correctly translated?
4. There is a ten year gap between Herod the Great and Quirinius in Luke.
This would help the Christians but it would throw the book of Luke off. The author is very specific.
Here are some of my main points again:
1. Nothing is known in history of a general census by Augustus;
2. I n a Roman census Joseph would not have had to travel to Bethlehem, and Mary would not have to travel at all;
3. No Roman census would have been made in Judea during the reign of Herod;
4. Josephus records no such census, and it would have been a notable innovation;
5. Quirinius was not governor of Syria until long after the reign of Herod.

You be the judge.