Other mistake: McClane pulls out a 9mm Heckler and Koch MP5 submachine gun, aims it at the police chief and pulls the trigger. It's loaded with blanks but nobody except him knows that. The problem is that the police chief is surrounded by armed colleagues, and not one of them draws his gun in defence of his boss. In reality McClane would be riddled with bullets before he could pull that trigger. Not to mention an MP5 needs a blank firing adapter to use blanks (it fits on the muzzle via three lugs), none is fitted on the gun in the scene. As a blank firing prop gun it would use a hidden internal restrictor, but that wouldn't be feasible if it was meant to be able to switch between blanks and regular ammunition, as it's supposed to in the movie.
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)
Factual error: The plane from which Bruce Willis escapes by using an ejector seat is a non-existing plane. The fuselage is from an old transport plane from the US Air Force made by Chase. But there has never been a Chase with 4 engines buried in the wing. America uses underslung engines. In this case, it is the wing of an Arado Blitz prototype from the second world war and the fuselage of a Chase cargo plane. (01:15:10)
Deliberate mistake: When the terrorists shoot a man in the church and he falls on his back, both benches behind him topple (in the shot from the ceiling of the church). You can't see that the benches are connected and even if they were, the bench he doesn't actually touch wouldn't topple. (00:07:35)
Factual error: In the scene where Bruce Willis faxes the finger prints of Oswald Cochrane to Sgt. Al Powell in LA, I don't see how you can determine the prints through a fax. They would appear as blobs on the other end, especially with faxes of that era. (00:24:45)
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 the bad guys 747 is blown up it is about 40 or 50 metres off the ground and travelling at take-off velocity, yet when Holly's plane is landing you can see that the debris field is perfectly circular. Surely the 747s speed and angle of descent would mean the debris field would be elongated? (01:50:30)
Factual error: The chase scene involving the snowmobiles is problematic in that McClane can actually see where he's going. In driving snow, it's often difficult to see, as snow blows in one's eyes. On a speeding snowmobile, in heavy snow and with no eye protection, it would be practically impossible to see anything. (01:31:15)
Continuity mistake: When McClane is lying on the conveyor, and he picks up his gun, just before the camera switches to the terrorist, you see the slide on the Beretta go back into the empty position, but when the camera changes, you hear another shot from McClane's gun. (00:13:15)
Continuity mistake: When McClane lights the torches on the runway he is surrounded by rough snow, then the long shot shows a smooth runway in the snow, then when the plane crashes the pilots see the tarmac with no snow, then the outside shot of the plane crashing shows the runway covered with snow again.
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.
Continuity mistake: John McClane and Major Grant are fighting on the wing of the aeroplane, and Major Grant's mouth gets extremely bloody. The shot switches to McClane and then back to Grant, whose mouth is still bloody. However, after the shot switches back from McClane to Grant, Grant's mouth is no longer bloody. (01:47:10)
Continuity mistake: When John is coming out of the drain on the runway, in shots facing him it's snowing, and in the shots that face both John and the plane, it's snowing. Yet, when the camera is just on the plane it's not snowing. (01:13:30)
Continuity mistake: Two guys dressed in red go to the church and are let in by the old man. One of the men then says something like "You were right about that," and the scene shows him shoot his gun with his arm outstretched (obviously). The next scene though of the old man falling backwards shows the shooter's arm down by his side, however in the next scene where it cuts back to the shooter his arm is outstretched with the gun again. (00:07:30)
Factual error: When the 747 explodes, fire is rushing up through the cargo hold. Esperanza - in the cockpit - looks back over his shoulder as if seeing the fire coming. Clearly he can't see the fire - since the view we are seeing is inside the cargo hold and cabin. But why is he then turning his head and looking back against the cockpit wall? And the flash we see on his face - from the explosion - that would not be there until the fire was inside the cockpit. And that would go so fast that he wouldn't have time to scream. (01:50:35)
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.
Factual error: There is absolutely no way the villains could remotely recalibrate the instruments on the plane itself. Even if it would be possible to remotely readjust the ILS glideslope - which it isn't - the pilot would've noticed their approach angle being suspiciously steep on the attitude indicator and the aircraft's radar altimeter would've given a terrain warning. (00:52:44)
Suggested correction: If the pilots are given an incorrect altimeter setting (outside barometric pressure), then yes, they can be fooled as to their altitude.
Factual error: At the time Die Hard 2 was made the only people in the Army that wore black berets were Rangers. If anything an SF (Green beret) team would be responsible for providing aid in that situation. (01:03:15 - 01:28:15)
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)
Suggested correction: Runway numbers are based on the magnetic heading of the runway, and since the earth's magnetic field is in constant motion, a runway's magnetic heading can and does change over time. As an example, my local airport's main runway is 30/12, but 10 years ago it was numbered 31/13. Therefore, it is possible that in 1990, what is now runway 30 at Dulles was numbered 29.
Random guesswork isn't a valid correction. A simple google search will show that runway 30 at Dulles has been called that since it was opened in 1962. In 1990 there were 3 runways at Dulles: 1C/19C, 1R/19L, and 12/30.