Revealing mistake: When the newscaster was filming Clinton giving a statement, the timer on the camera stayed at 0:00. The red "Rec" button, which supposedly was on, also looked fake. (00:10:35)
Continuity mistake: When the crocodile catches the man he bites his right foot off. 5 seconds later as he falls into the water his foot is back. (01:21:05)
Factual error: In the opening heist, the gang of thieves wants to steal "The Medal of Zeus." A plate at the museum explains that in Ancient Greece, Olympic champions were awarded olive wreaths, up to the 88th Olympics in 424 BC, when a golden medal was given to the victor for the first time. This last bit about gold medals is just made up by the movie. But it also gets the timeline wrong; the 88th Olympics were in 428 BC. 424 BC is when the 89th games took place. (00:03:30)
Other mistake: During the driving scene in the woods with the Bronco, at least two shots are reused twice.
Plot hole: When Mr. Shepherd arrives at the school he learn Joseph's (the student's) name but loses his memory. When they are telling him the nativity story Shepherd says "this Joseph" when referring to the student, but he shouldn't remember it.
Continuity mistake: Vincent and Oliver are eating ice cream, Vincent's ice cream cone repeatedly changes levels of ice cream left in his ice cream cone as he eats it. (00:48:00)
Revealing mistake: About seven minutes in, during the scene where we see Cooper helping the Nerd as a cameraman, you can tell that Cooper has been added to the scene using green-screen effects, as the actor was unavailable to shoot at the location. The lighting on Cooper doesn't quite match the lighting of the scene, and you can see a slight "blur/feathering effect" around him where the greenscreen background was removed.
Continuity mistake: Jay is mopping the floor after promising on the phone to his dad that he'll bring his non-existent fiancee to the wedding. He tries to talk one of the nurses into joining him. While doing so, he stands before her leaning on his mop with his left hand on top, which switches to the right hand between shots. (00:06:40)
Factual error: When the guy is talking to him on the phone and the Russian smashes it on the floor, the phone smashes and the battery comes out but the guy other end can still hear him. (01:04:00)
Continuity mistake: As the two assistant workers walk away from the prison building at the end of the first day, Charlotte Gainsbourg's grip on her folders switches between shots.
Continuity mistake: Felix pushes the fire alarm button and exits the building. As his buddy Danny reaches him, it's obvious that multiple takes of the scene have been made, since some extras that were meters ahead of him are just passing him by at the very first cut. (00:04:30)
Continuity mistake: The protagonist just unveiled to his boss the "nest" ad, to which he suggests some not-so-minor changes. Luca Argentero is holding the drape in two very different ways between shots (first with bunched cloth sticking up top, then simply folded). (00:05:00)
Revealing mistake: When the woman is tied to the bed, she is holding the ropes, and the rope isn't tight on her right hand; she can easily escape. (00:20:10)
Continuity mistake: In the observatory after the rain storm, Stanley lies down on a bench with Sophie sitting at the end of the bench. Later, when Sophie is walking around, Stanley has now moved all the way to the end of the bench where Sophie was sitting.
Continuity mistake: When Hugh Grant writes "Protagonist" on the board, the writing changes depending on the shot, most noticeably the G - sometimes it looks a bit like a backwards question mark, other times it's so slanted it looks more like an S.