There are: the obvious one being that Spud mentioned that these genealogies can be verified but he can't provide a robust and independent method for doing so - that is sufficient ground in itself to doubt his claim, without going anywhere near issues such as provenance.
But if I have DNA or photographic evidence, you're then going to want that verified - ad infinity. Luke and Matthew simply give what in those days probably was the equivalent of a birth certificate and the only way to identify someone, other than by their appearance.
The differences between the genealogies may even be evidence of their authenticity, since there were traditions in the OT to do with what happened when a blood line was about to end, either through childlessness or through only daughters being born.
In 1 Chronicles 3:17 Shealtiel is listed as the son of Jehoiachin (the same person as Jeconiah in Jeremiah and Matthew).
Luke however lists Shealtiel as the son of Neri.
Thus we could infer that the line of David's son Nathan was about to end at Neri, if the latter only had daughters or died childless. If Shealtiel was adopted as Neri's son or became Neri's son-in-law through marriage, this would have enabled the line of David's son Nathan to continue, at the same time as continuing the line of succession through Solomon.
If a similar thing happened with Jacob and Heli, this would account for the different post-captivity names in Matthew and Luke.
Another example of this is related in the story of Ruth, where her son Obed though Boaz is called the son of Naomi, Ruth's dead husband's mother.