Plot hole: When Andy turns into a werewolf, he kills both Amy and Detective Benbou. Later in the morgue, Amy tells him because of this that she is forced to become his "rotting sidekick." If this is completely true, then Detective Benbou should also be following Andy around but he isn't seen after Andy manages to escape from the morgue.
Continuity mistake: Much of this movie was shot in Luxembourg, not in Paris. This is obvious on several occasions - the road signs are clearly not like the French standard. You even see a sign to »Trier (Trèves)«. In Paris, there would be no signs to this German town...and even if there was, these would say »Trèves«. The buses also have French registration plates but are from Luxembourg companies.
Revealing mistake: When Andy and Claude are fighting each other in the train, during several shots, you can see Claude wearing gray briefs.
Other mistake: When Andy places the wedding ring on Serafine's finger after jumping off the Statue of Liberty, he places it on the index finger. Don't people usually put a wedding ring on the ring finger?
Plot hole: The Eiffel Tower is narrow at the top and gets wider on the way down, therefore any attempt to bungee jump from the top would result in massive injury or death from impacting the tower structure long before the ground was reached.
Visible crew/equipment: The boom microphone comes into the picture loads of times. It is most noticeable in an outdoor scene with the two main characters, during an emotional argument, the boom mic drops almost fully into the screen, complete with a gray fuzzy covering.
Other mistake: During the party in the church near the end the bad guy blocks the church door with a bulldozer. The girl climbs up to the top of the church, breaking off a stone gargoyle which lands on top of the bad guy while he's in the bulldozer. Then the girl climbs back down and gets into the bulldozer, which is completely undamaged from the gargoyle hitting it - the bad guy's body has completely vanished. She manages both climbs impossibly quickly.
Plot hole: Near the end of the film, at the big party in the abandoned church, one of the main characters is tied to a crucifix. In the ensuing mayhem, we see the crucifix fall backward, with the guy on top of it, facing the ceiling. In the shot where the panicked partygoers are fleeing, we see this guy running out of the church, carrying the crucifix, which is still tied to his wrists. So, how did he get up? And if someone stopped to help him, which seems unlikely, given the general panic, wouldn't it have been easier to simply untie him? The alternative would have been to hoist the whole kit n' kaboodle upright, which, at the least, would have taken two people.
Other mistake: When you first see the cop she has an English accent, the next time you see her it's a French accent.