Factual error: The plastic explosive used on the cockpit door was C-4. When shot (as shown), C-4 does not explode; it requires the use of a detonator.

Plot hole: At the start when the guys are infiltrating that building they parachute down to the roof. They are dressed in black so they can't be seen, but their parachutes are white. (Time)

Visible crew/equipment: In a scene midway through the film where Glenn Close etc receive the fax from the plane, the tracks for the camera can be seen on the floor.

Continuity: When Harrison Ford tries to enter the conference room when he comes upstairs from the lower level, he first struggles with the guard to the conference room door. While fumbling with the keys, the guard "wakes up" and shoots 2 shots toward Harrison Ford, where he turns around and shoots back. Those 2 shots from the guard leave bullet holes in the conference room door (the left door), and no one in the room gets shot from the bullets. Anyway the mistake is when Harrison finally enters the room, the bullet holes disappear. Whenever the bad guys return, the bullet holes are gone.

Other: 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.