Revealing mistake: Throughout the whole movie, bits of 'snow' stuck to various things in close up view (i.e. guns, hair, faces, clothing). Look closely at the snow, its quite obvious that they are actually little thin scraps of white plastic. Most evident is in McClane's hair when the platoon is about to move in on the church, the shot of him saying "You're not such an asshole, after all." (01:27:55)BillyBlake
Revealing mistake: When the soldier is lighting General Esperanza's cigar while Esperanza is still a prisoner in transport, the cigar is visibly already lit before the soldier's lighter brushes over the cigar. (00:24:30)
Revealing mistake: When the army guy opens the door on the 747 to climb out onto the wing, the outside door handle does not move and looks painted on. When the second guy re-enters the plane and shuts the same door, there is no locking mechanism shown on the sides of the door; it simply pushes open.
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.