Continuity mistake: When he's climbing down the vents, the strap unties, and Bruce Willis falls. He misses the vent he was reaching for, and falls past the next one, so we assume he catches the third one down. However, after he flicks off his lighter, the camera pans up from the lit vent to Karl, and we can see that he somehow grabbed and climbed into the vent he definitely fell right past in the shot from above. (00:48:30)
Continuity mistake: Takagi is sitting on the chair facing the door of the room when he is shot. In the next scene, the same door is splattered with blood, yet the glass structure which should be splattered with blood should be the glass window behind Takagi, not the door which he is facing. (00:30:15)
Character mistake: An unloaded automatic pistol is much lighter and balanced differently than a loaded one. When McClane hands "Bill Clay" (Gruber) the empty pistol, a terrorist of Gruber's credentials should pick up on the odd balance (I notice that difference, and I very rarely even pick up a gun).
Continuity mistake: When Powell's police cruiser is first fired on, he accelerates in reverse quickly. The first obstacle he hits completely destroys the right-hand side tail light assembly. Subsequnt shots of the car show the tail-light to be totally intact again. (00:55:05)
Visible crew/equipment: When Al goes into the lobby of the building, he walks over to a large reflective marble counter. If you look at this counter you can very plainly see the reflection of a large metal stage lamp hanging right over the actors' heads. (00:52:25)
Factual error: A few of Gruber's henchmen set up the rocket-launcher to blast the armored police vehicle. As one of them swings the legs of the launcher down, another uses a 'Hilti' gun to anchor the leg in place. A 'Hilti' gun is a construction device that uses gunpowder (usually a .22 shot) to 'blast' a nail into very hard material such as concrete. With the model they're using, the nail has to be manually loaded into the front of the gun for each shot before it can be used, however the guy using the gun never loads a nail into the gun. As it is, the result would be worthless.
Continuity mistake: When Powell is driving his cruiser in reverse to get away from the bad guys shooting at him, several shots show a full roll-cage in the car which is not there in any other scene or close-up of the interior. (00:55:10)
Visible crew/equipment: Everyone is surprised when Karl is alive at the end of the movie because he appeared to be dead when hanging by the chain that McClane had wrapped around his neck. However, if you look at the back of Karl's head during the entire scene, you can see the safety wire coming out of the back of his shirt that holds him up. No wonder he survived. (01:48:45)
Audio problem: Just after Hans addresses McClane by his name over the radio, we can hear Powell say, "Better get ahold of someone at dispatch," but his mouth movements don't match what we hear. (01:18:50)
Continuity mistake: In the scene where Al asks John if he has any kids of his own, John pulls out his wallet with a picture of his family. He is holding the radio and the wallet, but when it cuts to John's "Jungle Gym" comment, both his hands are on the wallet. It then cuts to John again holding the radio and the wallet. (01:16:35)
Factual error: When Willis kills the terrorist and throws him out the window onto the police car, the body lands on the windshield, and it shatters into little bits. The windshields on 80's cars were double paned with a thin, strong plastic between each pane, to keep them from breaking into little bits in accidents. Only the side and back windows would shatter like that. (00:54:45)
Character mistake: After the police scanner broadcasts the shooting at Nakatomi Plaza, reporter Richard Thornburg starts begging the station producer/director for a van and cameraman. This is as the evening news is about to go on the air. The floor manager is counting down, "We are on the air in, four, three, two, one...." as he is giving the hand signals to the news anchors. On a real television set, the verbal count would end at three and the mikes would go live. In this case, the floor managers "two, one" and all other words spoken after "three" would be heard by the "at home" audience. (00:58:45)
Factual error: The rocket-launcher used to destroy the LAPD Armoured car appears to be a French 'MISTRAL' infra-red homing, man-portable surface-to-air missile that is meant for shooting down aircraft and is not designed for a surface target role. Even if the missile seeker could acquire a surface target like the armored car as a correct infra-red signature (required before it will fire), its flight profile would not be suitable for attack and it would probably not even arm the missile warhead at such a close distance. The missile is also not re-loadable in the manner shown.
Visible crew/equipment: When McClane is crawling under the long table to get closer to hear the terrorists' conversation, you can see the reflection of the camera operator's legs following along with him on the table base. (00:29:15)