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)
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.
Visible crew/equipment: When one of the terrorists enters an abandoned floor, logically the floor should be empty, but you can see the casting crew in the reflection of the windows. (00:35:00)
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.
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up to the loading bay and a tail lift is deployed, but at the end when the ambulance is unloaded the tail lift has been replaced by ramps.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.
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?
Visible crew/equipment: In scene on the top floor after John hits the fire alarm, as he is seeing the fire trucks coming and then turns away, once the lights are turned on, you can see the reflection of a number of crew people in the window during/after the cut away. One dude in a green shirt, another in a white shirt are prominent. (00:41:00)