Revealing mistake: The whole time during the president's escape from AF1 (the scene where he's fighting with his corrupt agent) you can see through the airplane door that there is a loop in the movement of the water. It moves for about a second, and then stops, etc., etc.
Revealing mistake: When the fax machine is supposed to be printing out the incoming fax its LCD display shows that it is actually copying a document. The film crew must have pressed the copy button to achieve the effect of a piece of paper coming out. (01:16:05)
Revealing mistake: When Harrison Ford is dangling by a rope as he's pulled into the rescue plane, you can clearly see the entire wing of the plane through his legs as they pass in front of it.
Chosen answer: He fell out the back without a parachute when the door blew open. We see him both tumble off the ramp, and another shot of him falling from below.
jimba