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?
Character mistake: A waiter offers John champagne but instead gives him what looks like red wine.
Revealing mistake: When John McClane jumps from the explosion in the elevator shaft, you can see that it is not Bruce Willis but his stunt double.
Continuity mistake: When Theo is at the computer, locking the building down, the pens in the pen holder keep changing positions throughout the various shots.
Continuity mistake: When John and Karl are fighting, after John is shot, the amount of blood on John's arm changes. When John's back is toward the camera there's hardly any blood, then when he's facing the camera his arm is covered in blood.
Factual error: Obviously done to spice up the action, but there would in no way be enough time for McClane to jump away when he sees the rising inferno of flames coming up the elevator, as it would be too fast and burn him to a crisp.
Revealing mistake: As Bruce Willis walks into Nakatomi Tower, which is solely occupied by the Nakatomi corporation, behind him can be seen the logo of Merryl Lynch, which had offices in the building used for filming.
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).
Deliberate mistake: For Hans Gruber's iconic death scene, Alan Rickman's fall was filmed at high speed (for slow-motion playback) against a green screen, and the skyscraper perspective footage was added later as background. However, while Rickman falls away from the camera in slow motion, papers are fluttering around him in the background at normal speed. This was done deliberately to make the shot even more surreal.
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)
Revealing mistake: The first time John walks up to the rooftop, he walks backwards to avoid the thugs' bullets and shelters behind a wall. Despite supposedly being barefoot his socks are very noticeable and wrinkle around the ankle.
Continuity mistake: Takagi leads John inside Holly's office. A shot later Takagi has moved several meters behind and is holding the door knob.
Visible crew/equipment: At the end when all of the papers are falling from the building, there is a wide shot. On the right hand side of the shot looks to be some kind of blower machine making the papers come out.
Character mistake: When John is informing the police about the terrorists, Franco tells Han "we have to find him and shut him up, he's telling them everything" and Hans says that they will, but then incorrectly refers to him as Fritz. Fritz is the long red haired terrorist.
Continuity mistake: Argyle is seen driving the limo around the garage after hearing that the terrorists have taken over the building. During that scene there are a couple of shots where the back window does not show anyone or anything in the back. But after the limo stops, he looks in the rearview mirror and the bear is sitting with it's head over the back of the seat. This would have been noticeable in the driving shots.
Continuity mistake: In the outdoor shot where the lobby is being blown up after John drops the explosives down the elevator shaft, the stairs in front of the building disappear for a brief second.
Visible crew/equipment: When the car and truck drive upto the building, the truck goes down a ramp - another moving shadow can be seen cast over the car, from the camera crew.
Continuity mistake: In the scene where Sgt Powell is entering his patrol car after checking the building, you can see that the spotlight is missing from the car exposing the mounting holes. However, after the body has landed on his car and he retreats rather quickly, the spotlight is back on the car.
