Continuity mistake: When John and Karl are fighting and Karl reaches for the gun lying on the floor, John legs it out of an open door. Karl fires two shots, the first hits John and the second sprays blood all over the door. (01:47:35)
Continuity mistake: After McClane "kills" Karl by hanging him with the chain, Karl can be spotted at the top of the stairs on the right side as McClane is reloading his gun. (01:53:30)
Factual error: Would pulling the alarm call the fire and police departments if the phone lines were disabled?
Suggested correction: While I'm not sure how the alarms contact the fire department, it's also important to note that when Karl cuts the phone lines, his brother is re-routing some of the lines. I believe the implication is that he was bypassing certain lines so that way emergency services and the phone company wouldn't get alerts that their phones lines were down at the plaza and send people to check it out. So it would makes sense to me that a fire alarm could still get a signal through the phone lines in that case. (I'm also presuming that the way the fire alarm sends its signal is different from how a phone call is made, since one is automated and not call-based).
Character mistake: In the infamous 'shoot the glass' scene, Alan Rickman, playing a German, commands to 'Schieß den Fenster', which is wrong in German because the 'Fenster', the window, has in fact the neutral article 'das' instead of the masculine 'den'. Also, it is not a window in German but a 'Fensterscheibe', a window pane. In German he would say 'Schieß auf das Fenster' ('Shoot at the window!') or 'Schieß auf die Scheiben' ('Shoot the window panes!'). (01:36:00 - 01:37:30)
Factual error: If the hose hanger isn't heavy enough to instantly yank McClane out of the window, but instead slowly pulls him down, then it should be light enough for McClane to simply stand up and reel it in. If his weight is enough to slow the hanger's decent, then that means it only weighs slightly more than he does. He should have no trouble standing up and walking backwards to pull the hanger back up. The mistake is that the hanger pulls him slowly at all, it should have yanked him directly out of the window the second the line ran out of slack because McClane is not anchored to the floor in any way. This scene suggest that the hanger is both heavy enough to pull McClane but light enough that McClane's weight significantly slows it, which is impossible.
Continuity mistake: During the fight between Karl and McClane, Karl shoots at John and it hits him in the shoulder. That wound then disappears and reappears several times throughout the movie.
Continuity mistake: After John McClain has jumped off the top of the building, and the firehose hanger has got stuck to the railing, he has stopped at the top of the window, but in the next shot he is near the middle. (01:51:55)
Revealing mistake: Having leapt from the rooftop, Bruce has his feet planted on the window. As he then goes to push himself back in order to smash the glass with his gun shots watch the rope. Someone above has kindly held the rope out several meters away from the building in the next shot, allowing him to get a much bigger swing.
Factual error: Cutting through phone lines will not electrocute you. At best there a 80v AC ringing current per line which gives a mild shock. Also, when the technical expert kits the data cabinets the sensitive electrical equipment is highly unlikely to explode in a shower of sparks.
Factual error: The news reporter is listening to the police scanner, when Willis is heard talking, the channel lights that blink on the scanner are supposed to stop on the channel being used, but they keep flashing. (00:55:50)
Revealing mistake: Bruce Willis jumps off the roof with the firehose. The hose hanger breaks off the wall and apparently gets stuck in the railings. The shot is very careless: slow motion shows that the firehose doesn't get stuck, but simply clings like a magnet to the top of the railings. (01:51:50)
Continuity mistake: When John and Al are talking, if they have any kids, there is a shot of John's family in his wallet and you can see both thumbs on the wallet. The scene cuts away to John talking, and his left hand is holding the walkie-talkie. There isn't enough time for John to grab the walkie and start talking into it.
Visible crew/equipment: When John gets out of the limo at Nakatomi Plaza, a stage light is reflected clear as day in his door. (00:08:10)
Continuity mistake: When the FBI shows up and Duane Robinson is explaining to them what the police know, Al tells the FBI about John. Duane is in front of Al in the shot looking at the building, and right next to him in the opposite angle.
Visible crew/equipment: The shadow of the camera is visible right of screen when John is wrapping himself with the fire hose and asking himself why he's doing it. It lingers for some time. It looks to be a steadycam with a monitor.
Continuity mistake: Hans leaves his gun and flashlight lying on the ledge out of sight. When he edges back to get it, the gun is upright, easy to grab.
Revealing mistake: When McClane is on the roof shooting over the hostages the helicopter appears and they start shooting at McClane, the squibs used for the helicopter shooting scene are visible lying on the roof and explode in sequence, starting at the back and moving toward the camera as McClane does.
Continuity mistake: When McClane goes onto the roof at the end he shoots Uli as he opens the door and the blood splatters all over the wall at the side, but when McClane walks past the body there is no blood on the walls or steps or where the body is lying.
Continuity mistake: When the terrorists arrive the truck reverses up to the loading bay and a tail lift is deployed, but at the end when the ambulance is unloaded the tail lift has been replaced by ramps. Tail lifts are bolted to the truck frame and simply cannot be removed.
Visible crew/equipment: McClane runs up the stairs and looks on floor 31. He goes up another floor as the camera follows. The camera operator's shadow is blatantly visible left screen.