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.
Continuity mistake: In the airport lobby, when the two policemen come at the bar they have "snow" all over their clothes. In the next shot they are shown from behind sitting at the bar and Lorenzo's brother has no snow on his jacket. Seconds after Mc Clane comes to talk to them and the cop has snow on his shoulders again.
Continuity mistake: When McClane grabs Marvin the janitor and pushes him against the lockers, McClane's thumb changes position on the gun, some shots it's on the hammer, other shots it's around the handle.
Continuity mistake: When John and his wife hug, his hand suddenly appears on her head.
Continuity mistake: When Barnes and the SWAT team reach the Annex Skywalk, they get on the moving sidewalk. Before the terrorist stops the moving sidewalk by pressing the button, the sidewalk is already stopped, even though the light was still green at the time.
Continuity mistake: When the general exits the plane with Colonel Stuart, nobody shuts the door. It is closed in the very next shot.
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.