New this month Other mistake: When Bond enters the ruins of the old MI6 building, he encounters the plaque that lists all of those that gave their lives in service of MI6. In Skyfall, M mentioned this plaque, and mentioned that Silva's (the antagonist of Skyfall) name was Tiago Rodriguez, and that his name is on that plaque, and that she'd have it struck from the plaque. However, she never had the chance to do so within the timeline of the film (almost immediately after she said this, Silva escaped and tried to kill her at the government hearing, after which she escaped with Bond to Scotland, and died there). His name, however, is absent from the plaque, and there isn't even a gap for where his name might have been even if she *had* had the chance to have it removed.
Other mistake: The sealed off room in the L'American hotel is a fantasy. For one, a maid or the owners should spot that a room is missing from their own hotel. Secondly, we know that Mr. White visited frequently, and as recently as the events in Casino Royale as evidenced by Vesper Lynd's interrogation tape. Whilst it's conceivable he was able to secure the same room every year, that he was able to replaster and repaint the wall as well stretches belief.
Other mistake: During the plane chase near the end the cars go off to Bond's left, then he has to avoid the trees and turns left himself, then we see the cars are way over to his right and the trees have disappeared. The cars have no time to get that far over to the right - Bond should have seen them when he turned left himself.