Revealing mistake: John McClane stands in a little pool when the helicopter falling from the roof explodes outside and the windows shatter. In a short shot you see that this man is definitely not Bruce Willis. (01:52:50)
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)
Continuity mistake: When Bruce Willis shoots Alan Rickman, Rickman falls through the window and grabs Bonnie Bedelia's arm to pull her with him. He has a good grasp on her arm because of her watch. When Bruce Willis is trying to release the clasp on her watch, you see blood on her face from his arm. The shot then cuts to Alan Rickman, and when the camera goes back to Bedelia and Willis, there is no longer any blood on her face. (01:57:15)
Other mistake: Powell says he has a desk job, but he is driving a cruiser. Cruisers are for cops on patrol. A cruiser would not be issued for a cop at a desk, especially not one who's on his way home, as Al says he is.
Continuity mistake: When Hans takes Holly hostage, as she is sitting on the floor talking to Hans, as the camera goes from him to her, each time Holly's shirt is unbuttoned and open more so her bra and boobs are revealed.
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.
Other mistake: After Powell frantically radios in his distress call, other police cars converge on the street in front of Nakatomi Plaza, blocking off both sides of the street. But when McClane grapples down the building using the firehose, you can see traffic on the street below and none of them are police.
Other mistake: Near the start of the film, when John goes to meet his wife at the office block, there is a party going on and a small orchestra playing. When Gruber and his gang enter, the orchestra are still there. Gruber locks down the building, and takes the guests hostage. Where does the orchestra go after that? They are never seen again, even when the hostages are taken to the roof.
Other mistake: In the computer room shoot-out the bad guys shoot out all the glass room dividers in a hail of bullets, but the glass windows on the exterior of the building (behind the dividers and in the path of the bullets) stay intact; they don't even get scratched.
Continuity mistake: When the terrorist Karl is about to kill the man in the front desk, his fringe changes from neat and combed to slightly messy from one frame to the other.
Plot hole: After they shoot the glass and McClane escapes, the terrorists all just leave. There are limited ways out of the room, there must be a blood trail over the glass, he's moving slowly...and they let him go.
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.
Suggested correction: Hilti sells powder actuated fastening guns with collated fasteners and gunpowder shots lined up. Usually one can fire 10 rounds in a magazine. The gang would have probably selected such a model for this feature.
But that specific collated gun was not the one they were using.
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).
Suggested correction: This presumes that a person can notice the difference between a fully-loaded pistol versus a pistol that is empty, which makes sense. However, it would be much more difficult for a person to tell that a gun is completely empty versus one that only has one or two bullets loaded. Since Gruber has no way of knowing his ruse didn't work, he doesn't believe McClane would have given him a completely empty gun. He obviously believes there is at the very least one bullet in the gun. He's not planning on getting into a shootout with McClane, he is just planning to threaten him and he certainly doesn't need a fully loaded gun to do that.
Suggested correction: It's easy to tell the different between the weight of a loaded vs. unloaded pistol, but given Hans had never held the pistol before, he had no way to compare the weight. Unless he regularly handled that particular model of pistol (unlikely, given his pistol is a completely different make and model) he would have no point of reference.
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: 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.
Continuity mistake: When McClane has killed the first terrorist and sends him down the lift, McClane is hidden in the lift shaft. During the ensuing conversation McClane writes the names "Hans" and "Karl" on his wrist in permanent marker. This disappears in the next scene.
Revealing mistake: Even though there is no light shining on John McClane during the fight with Karl, there are several shots where it's obviously not Bruce Willis, but a stunt double.
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.
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.
Other mistake: When John is on the roof being shot at, he shoots the lock off a door before charging through it. We see a close up of the door as it's shot, and there's a blood smear already on it. He then goes through it shoulder first, which is what would leave a smear like that - must be from an earlier take.