Revealing mistake: In the skywalk scene, when McClane pushes the paint stand on the terrorist, it is quite obvious that they use a dummy when the paint stand falls on the terrorist and crushes him. (00:45:05)
Revealing mistake: Obvious stunt double for the black terrorist during the fight with McClane in the baggage area. He looks younger than him and has a different hairstyle. (00:14:10)
Revealing mistake: On one of the first shots of inside Holly's plane, you can see the blue screens through the windows. No, it's not blue sky, in all the following shots the sky outside is orange. (00:16:30)
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)
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.
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 John is fighting in the baggage area and he and the bad guy fall off one of the conveyors, you can see it is not Bruce Willis as he's falling. (00:15:00)
Revealing mistake: Right after they realise they have to get the planes in a holding pattern to clear the runways of snow, you can see a shot of Holly's plane. This is a model (Look at the clouds; they don't change shape that fast) and the fact that the lights on the wings are flipped. The right wing always has a green light, the left wing always has a red light. In this shot, the lights are reversed but not the logo. So it's not a mirrored image; it is a model. Also the lights on the top are LEDs in a strip. (00:27:38)
Revealing mistake: When the terrorists cut the pipes with wires behind the church, one guy uses a chainsaw, and the pipes he cuts are all empty.
Revealing mistake: McClane jumps out of the helicopter at the end and lands on the wing of the larger airplane. The stunt man who does this then proceeds to move up to a long wire on the side of the wing. Any normal airplane would not have a long wire on the wing.
Suggested correction: The terrorists in the film planned extensively for this operation, but the storm occurring may have just been a coincidence for them. They may also have had the plan waiting for a perfect opportunity, like a snowstorm. In the beginning of the movie, there's a news story on while the Colonel is exercising nude. The story says Esperanza's extradition has been long and drawn out, until a phone call from..." and he cuts the TV off. Given his connections, Colonel Stewart may well have been able to arrange a State Department call the week of a predicted snow storm. Esperanza's adherents may also have been able. Another scenario they may have had is to take the Air Traffic Controllers hostage (as they did) and have the other aircraft diverted for a supposed emergency, but the snowstorm worked out. Whatever the case, that element of the plot is an interesting discussion, not a mistake.
If the storm hadn't hit the pilots of the stranded airliners could easily have diverted to any one of half a dozen alternates, 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 the Esperanza's plane? They'd have it shot down.
That bothered me too when I first saw this in theatres. The chances of it snowing in D.C. on any particular day are pretty low, and the plan falls apart without it. The only way to 'fix' this is to assume that when the film was originally written, it was set in New York City. This makes more sense thematically...with the original set in Los Angeles. But at some point, probably late in the production, they changed it to D.C. for some reason, and made it fit as best they could.
The snowstorm was not part of the plan. Early on when the group of terrorists is sitting around the table about to exchange the package, Cochran is listening to a weather report and states that a huge storm is approaching, which makes the other men smile and one of them responds "God loves the infantry." The terrorists could still crash planes without the snow storm because they could impersonate the tower. The planes that are circling overhead are the planes that didn't have enough fuel to be diverted to another airport and that has nothing to do with a snow storm. The blizzard was simply fortuitous for the terrorists.
BaconIsMyBFF
The airliners we see could easily glide to any one of seven nearby airports from the airspace over Dulles, let alone fly there when fuel began running low.
That is a separate issue (and is indeed a mistake in the film) that doesn't really have anything to do with the blizzard. This film acts as if Baltimore Washington International or Richmond International Airport don't exist.
BaconIsMyBFF
And since they do, it is both a plot hole and a factual error. If they had called their fictional airport Springfield International, fine, but they didn't. They identified it as Dulles International which is within easy flying - or gliding - time to half a dozen other airports.
This is possible that other airports were closed due to bad weather.
Which necessitates the terrorists knowing that! They had to know the storm was coming for their plan to work. The stranded airlines could easily have diverted to an alternative even if that meant gliding, and they could do so without consulting air traffic control.
The terrorist obviously knew that. They are very arrogant and planned everything very accurately. They knew that other airports are closed because of the bad weather.
The airports were closed AFTER Esperanza's flight took off. The storm is an essential part of the terrorist's plans. Storms like the one we see can can diminish very rapidly or veer away from their original course (I have seen both happen) and cannot, ever, be counted on to the meticulous extent the terrorists do.