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)
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.
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)
Plot hole: There is no way the airport personnel could have kept everything going on quiet from the thousands of civilians in the airport. Even if nobody heard the shootout between McClane and the terrorists at the baggage area someone would have found out about the crashing of the Windsor flight.
Factual error: There is absolutely no way that Bruce Willis could have stood in the middle of an airport landing zone trying to keep the plane from crashing into the ground. He has no protective ear equipment on - that noise most definitely would have blown his eardrums out and blew him several yards away physically when it flew over him.
Revealing mistake: Right after they realise they have to get the planes in a holding pattern to clear the runways of snow, you can see a shot of Holly's plane. This is a model (Look at the clouds; they don't change shape that fast) and the fact that the lights on the wings are flipped. The right wing always has a green light, the left wing always has a red light. In this shot, the lights are reversed but not the logo. So it's not a mirrored image; it is a model. Also the lights on the top are LEDs in a strip. (00:27:38)
Factual error: There is no Glock 7, and Glocks are produced in Austria, not Germany.
Revealing mistake: When the terrorists cut the pipes with wires behind the church, one guy uses a chainsaw, and the pipes he cuts are all empty.
Continuity mistake: While Barnes is brainstorming ideas with his staff about using the marker beacons to communicate with the circling planes, he has a pen in his right hand held to his face. The next shot he turns, but the pen is no longer in his hand and his hand is nowhere near his face.
Factual error: A dangerous prisoner like Esperanza would not be flown into a civilian airport. He would be transported to the nearest USAF base, in this case Andrews Air Force base, always assuming that he is being extradited to Washington D.C.
Continuity mistake: When John and his wife hug, his hand suddenly appears on her head.
Continuity mistake: When the general is coming in for a landing, one of the bad guys is standing next to the radar display in the middle of the church. He appears to be doing something with the radar. The angle cuts, and he's now sitting down.
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: If the pilots are given an incorrect altimeter setting (outside barometric pressure), then yes, they can be fooled as to their altitude.
Even if the pilots would've been given an incorrect QFE for the barometric altimeter, the radio altimeter would've still given the correct altitude, and there's nothing the bad guys could do to mess with it.