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)
Revealing mistake: After escaping from the roof, John walks inside the building. When he runs towards a huge vent his bare feet swap to wearing black shoes.
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 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.
Continuity mistake: After John has crawled through the vents and enters the room where Hans shot Takagi, the amount of blood on the window is a lot more than was thereafter Takagi got shot.
Continuity mistake: In most of the film Bruce Willis' shoulder scar (from surgery when he was 17) is on his left, but as he is looking out the window just before SWAT comes in, it's on his right, clearly a flipped shot. (01:11:40)
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.
Visible crew/equipment: As the terrorists arrive, there is a shot of two vehicles pulling up. The camera is tracking along with the vehicles. At the very end of the shot its shadow and a crewmember's shadow are visible on the concrete.
Visible crew/equipment: When McClane steps out of the Limo at Nakatomi, a large film light is reflected in the door.
Continuity mistake: Karl comes in to tell Hans that Marco is down on the street and that the bag is missing containing the detonators. Hans then picks up the radio and switches channels to talk to Theo. Right after that we hear Powell on that same channel trying to reach out to John. How could Al be on the same channel as Theo when Hans was just talking to John minutes before on a different channel?
Answer: The most likely reason is that the two versions have been "panned and scanned" differently. In the original theater version, both things are on screen at the same time at opposite sides of the screen. In one version, the person who did the TV P&S (not someone associated with the making of the film) chose to move the view from one side of the original picture to the other, showing the terrorist, while the person who did the VHS P&S stayed focused on one side of the frame, only showing Al.
Myridon