[John throws a body onto a cop car to get his attention.]
John McClane: Welcome to the party, pal!
At the end, Karl emerges from the building and tries to kill McClane, only to be gunned down by Powell. The triumphant music which swells as Powell shoots him is from the "Aliens" score--it plays at the end of that movie when Bishop reappears in the dropship to save Ripley and Newt, after they think he's abandoned them. See more...
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Revealing: In the shot where we see all the terrorists (except Karl and Theo, who are upstairs) walking into the building from downstairs, they are about to walk through a doorway when the camera cuts out. Watch the terrorist on the left (he's the one who guards the door) - before the camera cuts out he realises he's about to hit the doorframe very hard. Reminiscent of the Stormtrooper in Star Wars.
Continuity: When Bruce Willis shoots Alan Rickman, Rickman falls through the window and grabs Bonnie Bedilia'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.
Revealing: Bruce Willis wore fake feet during the movie to protect his own while shooting the film. They were like boots that slipped on over his. At the part where the FBI guy shoots at him from the helicopter and Bruce jumps to a lower level of the roof, you can see the tops of the fake feet that aren't tight around his ankles.
Continuity: After the terrorists blow the roof and Willis jumps off with the fire hose, he hits the window. After kicking the window for a while, he decides to shoot it. As he pushes off the window you can see that his gun is out and pointed at the window yet in the next scene he pulls the gun from his side and then starts shooting at the window.
Visible crew/equipment: In the first scene of the Christmas party when Takagi steps out of one the offices and greets couple of his guests, the camera pans left to show the orchestra and other guests. A huge shadow of the camera and its operator is being shown in the backwall, then the stagelight gets moved to light a different area and the shadow is gone.
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.)
Other: 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.