Revealing mistake: When Hans discovers the first bad guy lying dead in the lift ("Now I have a gun - HO HO HO!") and pushes his head, the corpse is moving his head before he is hit (watch carefully). He also closes his eyes before Hans makes contact. (00:39:15)
Revealing mistake: 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. (01:50:30)
Revealing mistake: When the hostages are running down the stairs after the C4 explosion, a large, fist sized chunk of concrete falls on an older man's head and he just runs straight on. (01:52:35)
Revealing mistake: Having leapt from the rooftop, Bruce has his feet planted on the window. As he then goes to push himself back in order to smash the glass with his gun shots watch the rope. Someone above has kindly held the rope out several meters away from the building in the next shot, allowing him to get a much bigger swing.
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)
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.
Revealing mistake: When John jumps off the roof with the hose tied around him, you can see that the stuntman's hair is slicked back with fireproof gel during the explosion.