Character mistake: After the police scanner broadcasts the shooting at Nakatomi Plaza, reporter Richard Thornburg starts begging the station producer/director for a van and cameraman. This is as the evening news is about to go on the air. The floor manager is counting down, "We are on the air in, four, three, two, one...." as he is giving the hand signals to the news anchors. On a real television set, the verbal count would end at three and the mikes would go live. In this case, the floor managers "two, one" and all other words spoken after "three" would be heard by the "at home" audience. (00:58:45)
Character mistake: In the infamous 'shoot the glass' scene, Alan Rickman, playing a German, commands to 'Schieß den Fenster', which is wrong in German because the 'Fenster', the window, has in fact the neutral article 'das' instead of the masculine 'den'. Also, it is not a window in German but a 'Fensterscheibe', a window pane. In German he would say 'Schieß auf das Fenster' ('Shoot at the window!') or 'Schieß auf die Scheiben' ('Shoot the window panes!'). (01:36:00 - 01:37:30)
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.
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.
Character mistake: A waiter offers John champagne but instead gives him what looks like red wine.