Revealing mistake: In the skywalk scene, when McClane pushes the paint stand on the terrorist, it is quite obvious that they use a dummy when the paint stand falls on the terrorist and crushes him. (00:45:05)
Revealing mistake: Obvious stunt double for the black terrorist during the fight with McClane in the baggage area. He looks younger than him and has a different hairstyle. (00:14:10)
Revealing mistake: On one of the first shots of inside Holly's plane, you can see the blue screens through the windows. No, it's not blue sky, in all the following shots the sky outside is orange. (00:16:30)
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)
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.
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: 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)