Audio problem: In the climactic scene where the 747 is taking off, the general applies full power on the throttles and the engines spool up to full power as they should. However, in the next shot from the cockpit, the general is pulling back on the yoke, nobody's hands are on the throttles at all, and yet we hear a second (apparently) identical increase in engine power. Pulling back on the yoke has nothing at all to do with the engines - the noise we hear should remain at a constant level. (01:50:15)
Audio problem: When the terrorist at the church goes inside and asks "where's Cochrane", the other replies "he didn't make it." His mouth isn't moving.
Audio problem: When General Esperanza is trying to land the plane there's a hell of a lot of noise from the wind blasting in through the shattered windscreen. Yet when we see McClane listening in to his radio communication he can be heard completely without a trace of wind noise.
Audio problem: When McClane goes to Lorenzo's office for the first time, we hear Lorenzo say "who is it? Come in." His lips don't move (which you can tell despite his mug being up to his mouth).
Audio problem: John is on the wing of the plane, questioning why he is there. His mouth isn't moving with what he is saying.
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.