Continuity mistake: After McClane gets the car towed away, notice that it is night and snowstorming all over the place. When he enters the airport, you can see that outside it is daytime and sunny, yet McClane shakes off snow whereas other people in the airport don't have snow on them at all. The airport scenes were filmed at LAX's Bradley International Terminal during the month of February, so this explains the sunny day. (00:01:35)
Continuity mistake: Two guys dressed in red go to the church and are let in by the old man. One of the men then says something like "You were right about that," and the scene shows him shoot his gun with his arm outstretched (obviously). The next scene though of the old man falling backwards shows the shooter's arm down by his side, however in the next scene where it cuts back to the shooter his arm is outstretched with the gun again. (00:07:30)
Continuity mistake: In the beginning of the movie when John is sitting at a table in the airport smoking a cigarette, you see him notice the table with the 3 (2 white and 1 black) guys that are acting suspicious. When the black guy gets up to leave, he leans down and you see a hand grab a package. If you notice, the hand that grabs the package is white. Later when the two white guys leave, one of them leans down to grab the package and it's the same shot that was used when the black guy grabbed his package. (00:08:50)
Continuity mistake: When McClane is lying on the conveyor, and he picks up his gun, just before the camera switches to the terrorist, you see the slide on the Beretta go back into the empty position, but when the camera changes, you hear another shot from McClane's gun. (00:13:15)
Continuity mistake: The dead bodies of the SWAT team move around on the escalator between shots. The best example of this is after the last SWAT guy dies, there is a body or two near the end of the escalator. They disappear or at least move much further away after McClane drops his gun on the escalator. And all this happens while the escalator is not moving. (00:45:15 - 00:48:00)
Continuity mistake: When Col. Stuart is talking to Gen. Esperanza on the walkie-talkie about what runway to land on, behind Stuart you can see one of his men walk up to the map of the runways. Stuart turns around and starts walking to the map and the guy isn't there anymore. When Stuart gets in front of the map, the guy comes up and tells him which runway Esperanza should land on. (01:09:05)
Continuity mistake: Bruce Willis is emerging from an underground air-vent when the plane with General Esperanza is landing. Initially the plane is coming on a direct course for him and he struggles to get out. In fact the front wheel is on course with and knocks the vent cover. But in the very next scene, the tire marks clearly show the front wheel passed to the right of the vent and so completely missed it. (01:11:40)
Continuity mistake: When John is coming out of the drain on the runway, in shots facing him it's snowing, and in the shots that face both John and the plane, it's snowing. Yet, when the camera is just on the plane it's not snowing. (01:13:30)
Continuity mistake: When McClane is desperately trying to get out of the manhole cover to avoid the plane, he props it open with a steel bar. Moments later, just before the plane runs over it, the bar is gone, so there should be nothing holding it open. The size of the gap between cover and runway also decreases between these shots. (01:14:50)
Continuity mistake: When Richard Thornburg is in the aeroplane bathroom giving his live report, in a number of the shots he is holding the phone upside down. (01:37:00)
Continuity mistake: During the last fight scene on the wing of the plane, just after the guy is sucked into the engine, general Stuart comes rushing out and yells something like "it's time for the main event". At this, John rolls over onto his back. The shot then switches to much further away, and he is still on his stomach. The camera cuts in close again, and John is back on his back, and sliding towards the center of the wing. The camera cuts away again and shows John back on his stomach and just now rolling over. (01:43:40)
Continuity mistake: McClane's fireman's jacket gets progressively bloodier throughout the film, but around the time when he is fighting the terrorists on the planes wing, it is miraculously clean again. McClane is not wearing it, but it does get cleaner. (01:45:50)
Continuity mistake: John McClane and Major Grant are fighting on the wing of the aeroplane, and Major Grant's mouth gets extremely bloody. The shot switches to McClane and then back to Grant, whose mouth is still bloody. However, after the shot switches back from McClane to Grant, Grant's mouth is no longer bloody. (01:47:10)
Continuity mistake: When McClane is fighting Col Stuart there is an up close shot where McClane kicks the Colonel and the Colonel grabs his leg. When the camera cuts away he is holding McClane's arm instead of his leg. (01:48:40)
Continuity mistake: When Mclane is desperately trying to get his fallen Beretta from the conveyor, he flicks the on switch to the conveyor. The terrorist then sprints down the conveyor to try and get the gun before Mclane, and you can see in the first shot of the terrorist running, that he is virtually at the gun immediately. The camera cuts to Mclane, and then back to the terrorist who is now significantly further away from the gun than he was before.
Continuity mistake: When McClane lights the torches on the runway he is surrounded by rough snow, then the long shot shows a smooth runway in the snow, then when the plane crashes the pilots see the tarmac with no snow, then the outside shot of the plane crashing shows the runway covered with snow again.
Continuity mistake: In the beginning of the film when two of Stuart's men arrive at the church, their van stops and it is not snowing outside,same thing when they're shown knocking and then when the man opens the door. However, in the shot just after (which is taken from behind the door) snow is falling on them. The shot then switches to an outside view ,and it's not snowing anymore .
Continuity mistake: When the army truck arrives at the 747 hangar, we see a line of snow on the ground behind it. The actual truck has no snow on it at all, despite its journey to the hangar.
Continuity mistake: While Barnes is brainstorming ideas with his staff about using the marker beacons to communicate with the circling planes, he has a pen in his right hand held to his face. The next shot he turns, but the pen is no longer in his hand and his hand is nowhere near his face.
Continuity mistake: When the lady sitting next to Holly pulls out her stun gun, her book is resting against her stomach. However, in the previous shot from a different angle, the book isn't seen.
Suggested correction: Snow doesn't generally accumulate on a moving vehicle. Anything resting on the vehicle will blow off once it's in motion unless it's very wet and/or heavy.
As a truck driver, I can tell you that the conditions shown would have snow accumulating on a moving vehicle at least in some places.