Plot hole: If you don't have Jesus' DNA, only that of Mary Magdalene, how does it prove anything other than that Sophie is related to some lady? It would still not definitively prove Christ was married to her or that he was not divine.
Plot hole: The Louvre is home to art worth millions. Even with the electronic security measures in place the museum would be guarded around the clock by armed guards thus making the entire idea of the shooting of its curator and his killer escaping impossible.
Plot hole: Fache says he believes Langdon killed all those people because Aringarosa told him Langdon came to him in confession over the murders. We know Langdon made no such confession, so what made Aringarosa involve Langdon in the murders in the first place? Aringarosa never saw the curator's daily planner, his email, and wasn't there to see the message on the floor, so other than Langdon conveniently being in town for his book signing, why did Aringarosa name Langdon? If he was just telling that to Fache so he would have someone to arrest, Aringarosa could have named anyone.
Suggested correction: After Aringarosa is shot, Fache questions him and says (speculating) one of his followers saw the crime scene photos and called him, and the Bishop's response implied he was correct. Therefore, the Bishop knew Langdon was named in the floor writing before he called Fache, and given Langdon's work in the area of religious symbols it is very conceivable the Bishop knew who Langdon was, so named Langdon in an attempt to foil whatever Sauniere had intended.
Suggested correction: The book says, there's this guy 'the teacher' who knows a lot about what's going on. It's not unthinkable that Aringarosa heard it from him, so I wouldn't call this a plothole.