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)
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)
Factual error: Throughout the film, characters are able to break through on radio transmissions and speak to the other person talking, and the other person would hear them. In reality, they would have to wait until the first transmitter un-keyed the radio before any other discernable radio traffic could have be heard. (A good example of this is the scene where Ellis is giving up McClane.) (01:18:40)
Factual error: The shrink on the news refers to the Helsinki syndrome. This should be the Stockholm syndrome. Being an expert, he should know the difference, and there's no suggestion it's a deliberate oversight to imply a lack of knowledge. (01:25:25)
Factual error: The cops try to get in the building by cutting some metal part of the door, it might be the lock. All they have to do is break the glass. SWAT teams aren't going to worry about a bit of property damage with hostages' lives on the line.
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.
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.
Factual error: John McClane wraps a fire hose around his waist, uses it to jump 100 feet until the coil catches the lip of the building, and the hose catches him. This should have seriously injured him due to the inelastic material fire hoses are made of, and the fact that he was not wearing a safety harness, but he barely gets the wind knocked out of him.
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.
Factual error: The walkie talkies used are Kenwood TH21BT 2 meter VHF ham radio walkie talkies. Stubby rubber ducky antennas, if they are made for VHF, wouldn't transmit very far - likely they are UHF antennas which is even worse. The police dispatchers would not be listening to them on any Channel 9 on 2 meter or 440 Mhz ham radio. Also Al Powell would not have a radio for that in his car. If there was a Channel 9, an emergency channel, Hans Gruber's radio would not have been tuned to that during John McClane's rooftop call for help picked up by police - monitoring channel 9? Also on Thornberg's desk at the TV station there is a Kenwood TS-711 according to RigPix Database info (I thought it was an HF rig) - with the proper antenna it would allow Thornberg to communicate from his office with John McClane and the terrorists. But why would he need to do that? He doesn't seem to be the kind of guy to have an All Mode (FM, SSB, CW) VHF transceiver on his desktop. Probably most hams don't even have that. Maybe an FM 2 meter and 440, maybe an HF or HF and 6 Meters. But only a VHF all mode (expensive for single purpose) interested ham radio operator would have such a rig.
Factual error: When the police officer first comes to the tower and looks around there is a football game the terrorist is watching on television. The movie takes place on Christmas Eve. The Southern California vs. Notre Dame game, which is the one being played in the movie, is a classic rivalry game played in either late November or early October. This is especially true in 1988 as ND and USC were ranked 1 and 2. Notice the terrorist display displeasure when the announcer notes that ND just scored. USC is the home town team. It is also apparent that the game is being played during daylight hours, but at this point it is dark outside.
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.