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Continuity: Julia (Christina Applegate) puts a "Hello My Name Is..." sticker on Thibeau's tunic with her phone number on it. Only part of the sticker is visible. When he turns around to walk down the stairs, it is fully visible. A moment later when he stops the purse snatcher, it's gone. Three seconds later, talking to the woman dressed as a witch, it's back again.
Revealing: When they are driving back from the museum Thibault and Andre are both feeling sick and Julia asks Hunter to slow down. Hunter mentions that they are only doing 22mph and Julia replies "can you try going at 21?" However in the background a passer by is jogging past them - that's a pretty fast jogger.
Deliberate "mistake": Just after arriving in the 21st century, Thibault and André enter an elevator and scare away its occupants. Attempting to chase them, the elevator doors close despite their attempts to keep it open. Elevators have a safety mechanism which opens the door when they encounter resistance. This was ignored deliberately in the film for comic effect.