Revealing mistake: When the plane is delayed because the luggage got crushed, the sign changes their flight status to DELAYED. It's obvious that the one that changed is the only row meant to move. The letters are spaced out so that they can flip over but all the other letters have no spaces and actually look like stickers.
Other mistake: When Eugene, Raymond, and Frank Grimes get back into the car, Raymond and Frank get in the back seat, with Eugene in the driver's seat. During the conversation before taking off, Eugene keeps looking up and to the right to look at Raymond and Frank in the rearview mirror. However, there is no rearview mirror.
Continuity mistake: In the scene where Martin Short is in the clinic, he is talking to a fellow patient. The Spanish patient offers him a cigarette and while they are both smoking Danny Glover walks in. While Short and Glover are conversing, there is a shot of the Spaniard in the background smoking. Then the next shot (less than a second later) the Spaniard is lying down with no cigarette.