Factual error: In circling over Washington Dulles, a plane would fly over several airports that they could land at with perfect communication, including Richmond, Baltimore, Andrews AFB, etc. Also, there is no communication from the airport to the plane but the plane would be in range of no fewer than 15 transmitting stations that could have relayed messages.
Factual error: It is impossible for a stream of burning jet fuel to follow a plane through snow and catch up. Not only is jet fuel extremely hard to ignite, almost as soon as the plane was off the ground the fuel stream would be too dispersed for the flame to climb up into the tank, and even if not it wouldn't burn fast enough to catch the plane.
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.
Factual error: When McClane is trapped in the cockpit of Esperanza's plane, and the terrorists throw grenades in, it sure takes them a long time to explode, almost 30 seconds before he ejects from the plane and the grenades go off. Normal grenades have about a 5 second fuse. With a delay that long he could even have thrown them all back out at the bad guys.
Other mistake: The female journalist is called Samantha Coleman through the movie, but appears in the credits as Samantha Copeland.
Factual error: There is no airport in the world with a manhole cover in the middle of a runway. (01:14:00)
Factual error: The payphone McClane uses in Dulles airport has the "Pacific Bell" logo. Pacific Bell is a West Coast phone company. (00:04:20)
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.
Plot hole: The whole of Col. Stuart's plot to free General Esperanza and flee to a country with no US extradition laws would be rather impossible, as the plane with Esperanza and the terrorists would have been brought down by the US Air Force long before reaching international waters, especially given the fact that they would not maintain control over the airport landing systems after taking off.
Factual error: Firing a full magazine of blank cartridges from an automatic weapon in the police station office as McClane does would be painfully loud. Nobody shows the slightest effect - nobody even winces. Some of the men wince slightly but their reaction is grossly underplayed. Obviously the sound was looped in later. (01:37:40)
Factual error: After recovering a pistol from a slain baddie, John McClane explains to airport security that it's a "Glock 7" (in actuality a Glock 17) and says that it's made of porcelain that makes it "undetectable by X-ray." Excusing the fact that not only Glock, but no major firearms company has ever mass-produced such a weapon due to functionality issues, it doesn't change that the ammunition would still be visible on X-ray. The armorer for the production team pointed these facts out on set and tried to convince them to change this detail, but they filmed it with these mistakes anyway.
Factual error: When Holly's plane finally lands, the cockpit shot shows the pilot with his hands on four engine throttles. But Holly's plane is an L-1011 TriStar, which only has three engines. (01:52:00)
Factual error: At the end when John lights the fuel with a lighter, this isn't possible with Jet A-1 which is what the Boeing 747 is fuelled with. This type of fuel is extremely hard to light. Even if you drop a match into a bowl of jet A-1, it will not ignite. Jet A-1 has to be compressed or have its temperature raised to a minimum of 38c/100f in order to ignite (which the compressing also does) so fuel in snow would never ignite in the way shown.
Plot hole: When they try to contact the planes using the air phones, they say there are 18 planes but only 5 have airphones, and they got through to 3 of them, but they're trying to contact the others. Nothing the terrorists did kept the planes from talking to each other, so there is really nothing keeping the informed planes from radioing the information to the other pilots. (01:04:00 - 01:04:50)
Factual error: Near the beginning of the film when John McClane goes to the pay phone and calls his wife Holly on the airplane, that was impossible at the time. Those phones you see on the seats on the plane can only be used from the air to the ground not the other way around. Holly does answer on the plane phone and not on any cell phone she had in her purse. Not to mention even if it was possible to call the planes from the ground, they could do that to warn them of what's going on below and prevent more crashes. (00:04:20)
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)
Factual error: Several runway numbers are mentioned in the movie: runway 10, 15, 25 right and 25 left. Runway 25 means course 250. The opposite end would then be Runway 7 (course 70). It would be unusual for an airport to have runways running course 70, 100 and 150, as that is way too close. And Dulles certainly does not. In the church occupied by the terrorists, the radar display (the upright one with the circular LED pattern, not a scope) shows the runway configuration of Las Vegas McCarran airport, not that of Washington Dulles airport. McCarran does have runways 25R and 25L, which are mentioned in the film.
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: 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)