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: 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 the terrorist clears the nearly fuel-exhausted plane to land on the lowered ILS, the terrorist says, "Windsor 114, you are cleared to land on Dulles Runway 29, ILS." Problem is: There is no Runway 29 at Dulles. The closest runway alignment for a 290 degree heading is Runway 30. (00:53:35)
Factual error: When McClane lights the fuel with the zippo, the flame trail is all wrong. There appears to be a thin strip of fuel which accelerates away from him. However, we have seen the Fuel spurted out in a wider less controlled manner from a wing tip that has to be at least fifteen feet up, in a wind, which would have sprayed it around further. There is no way it would light in the tight manner shown. (01:45:55)