Continuity mistake: When Mundy and Claire are sitting in the car outside the apartment building, the rear view mirror has disappeared (probably removed to prevent it from obscuring the actors' faces). It mysteriously reappears later on.
Continuity mistake: The professor translates the two Chinese symbols from Mundy's brass rubbing. Then he's shown a Chinese business card, and states that the 12 symbols on the card say the same thing. But not one of the symbols on the card matches the first two from the paper.
Continuity mistake: When the airline pilot enters first class to announce the baggage search, we see only 7 seated passengers and many empty seats. When the angle reverses, there are instantly 15 people seated, and almost no empty places.
Continuity mistake: While he hangs from the ceiling over the jewels, Al's trapeze is spinning slowly. But when the shot cuts to a close-up, you can tell from the stationary background that the trapeze is now perfectly still. In the next full shot, though, it's spinning again.