Deliberate mistake: When the terrorists shoot a man in the church and he falls on his back, both benches behind him topple (in the shot from the ceiling of the church). You can't see that the benches are connected and even if they were, the bench he doesn't actually touch wouldn't topple. (00:07:35)
Deliberate mistake: At the very end, John McClane lights the fuel trail which subsequently engulfs the plane. To do this, he tosses a lighter onto the trail which begins six inches from where he lies, having fallen from the wing while pulling the lock off the fuel dumper. Trouble is, the fuel began flooding out at the same time he fell, and the velocity would carry him some distance forward on the ground after he lands (which it visibly does); hence, it is physically impossible for him to be in the position he is in relation to the fuel. (01:50:05)
Plot hole: The only reason the terrorists' plot can work is that the airports around Dulles are all closed to landings because of the violent snowstorm. If there were no storm, the pilots of the airliners in the holding pattern would simply divert to nearby airports when they started running low on fuel. If they were able to do that, the whole plot would simply fall apart. How were the terrorists able to count on the storm happening on the very day General Esperanza's flight was due to land? They didn't have any influence over the date of his flight. How did they know the storm would be so bad that all airports would be closed - except Dulles? I don't think they had any way of predicting the weather quite that accurately, and If the storm hadn't hit or had been even slightly less severe the pilots of the stranded airliners could easily have diverted to any one of half a dozen alternate landing sites, including a nearby Air Force base. They could do this without consulting or even contacting air traffic control. The whole plot falls apart from there - no hostages, no leverage, and who cares what happens to the people on Esperanza's plane? They'd have it shot down as soon as they knew Esperanza had killed the pilot and taken over the flight.