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.
Suggested correction: You can see him applying a detonator prior to him shooting it.
If he applied a blasting cap (detonator) he should have used it then. Just putting a detonator into C-4 doesn't all the sudden make it vulnerable to being shot, he would have to actually hit the blasting cap's wire, which is about 5mm thick and relatively short (and it would have to be one that's sensitive to gunfire). Not a very probable shot, even less so when he doesn't even look when he shoots.
Continuity mistake: In the scene where the President is being escorted to the escape pod, there is an extra shot where the President is hiding on his own around the corner from a terrorist, who is sneaking around in the background looking for him. In both the preceding and following shots, the President is being physically escorted by two Secret Service men who are pulling him along and forcefully holding his head down. This shot is wrongly inserted into this portion of the scene and needs to be later in the film, when the President is trying to escape. (00:23:40)
Suggested correction: This mistake does not occur in the film.
It is a fragment of the scene when the man is checking downstairs when the whole plane is to be re-checked.
Plot hole: After the President sabotages the fuel pumps, two of the bad guys go down and manage to repair the damage. They then proceed to go back upstairs and (supposedly) lock the President downstairs... Where he would be free to simply sabotage the fuel pumps again.
Suggested correction: Harrison Ford tricks the other Russian watching the conference room door and holds him at gun point to escape the cargo hold, you can't miss it.
The point by the poster is that the guys who fixed the sabotage didn't know the president had escaped, so they thought they were locking him in the lower compartment where he could then just sabotage the plane again.
Factual error: The passenger door at the front of a 747 opens outwards and towards the front of the plane (as seen when President Marshall boards the plane). When the first family is being evacuated at the end of the movie, the door is nowhere to be seen.
Suggested correction: That's because Gibbs had blown the emergency lock on the door and it went flying. Now, whether they'd actually do that and risk the door flying through the engine is another story, but I doubt the engineers had a mid-air rescue in mind when they designed it.