Character mistake: When airport control makes the call to "change the boards" to delayed, Auckland (New Zealand) is spelled Aukland.
Plot hole: When they try to contact the planes using the air phones, they say there are 18 planes but only 5 have airphones, and they got through to 3 of them, but they're trying to contact the others. Nothing the terrorists did kept the planes from talking to each other, so there is really nothing keeping the informed planes from radioing the information to the other pilots. (01:04:00 - 01:04:50)
Revealing mistake: In the skywalk scene, when McClane pushes the paint stand on the terrorist, it is quite obvious that they use a dummy when the paint stand falls on the terrorist and crushes him. (00:45:05)
Factual error: The terrorists are using Kenwood 46AT Handheld Radios that operate on 440Mhz. The Army moves in with a Kenwood TS-850 Radio that operates on 30Mhz-3Mhz. Nowhere near the frequency that the terrorists are using. (01:11:30 - 01:25:40)
Factual error: At the end of the movie, all of the planes come in to land by the fire. However, the planes are far, FAR closer than any large aircraft would land to each other. FAA regulations would have the aircraft about 5 miles away from each other. If they're landing this close due to "emergency", there would be wicked wake turbulence at such close distances.
Visible crew/equipment: When we first see McClane on the snowmobile, marks from the camera snowmobile are visible. (01:27:20)
Continuity mistake: After McClane gets the car towed away, notice that it is night and snowstorming all over the place. When he enters the airport, you can see that outside it is daytime and sunny, yet McClane shakes off snow whereas other people in the airport don't have snow on them at all. The airport scenes were filmed at LAX's Bradley International Terminal during the month of February, so this explains the sunny day. (00:01:35)
Audio problem: When the terrorist at the church goes inside and asks "where's Cochrane", the other replies "he didn't make it." His mouth isn't moving.
Revealing mistake: Obvious stunt double for the black terrorist during the fight with McClane in the baggage area. He looks younger than him and has a different hairstyle. (00:14:10)
Other mistake: McClane pulls out a 9mm Heckler and Koch MP5 submachine gun, aims it at the police chief and pulls the trigger. It's loaded with blanks but nobody except him knows that. The problem is that the police chief is surrounded by armed colleagues, and not one of them draws his gun in defence of his boss. In reality McClane would be riddled with bullets before he could pull that trigger. Not to mention an MP5 needs a blank firing adapter to use blanks (it fits on the muzzle via three lugs), none is fitted on the gun in the scene. As a blank firing prop gun it would use a hidden internal restrictor, but that wouldn't be feasible if it was meant to be able to switch between blanks and regular ammunition, as it's supposed to in the movie.
Continuity mistake: When Col. Stuart is talking to Gen. Esperanza on the walkie-talkie about what runway to land on, behind Stuart you can see one of his men walk up to the map of the runways. Stuart turns around and starts walking to the map and the guy isn't there anymore. When Stuart gets in front of the map, the guy comes up and tells him which runway Esperanza should land on. (01:09:05)
Factual error: After the fight with Colonel Stuart on the wing of the plane, Bruce Willis falls down from the wing. As he falls, watch the tyre-tracks near him. Those are definitely NOT the tyre-tracks of a plane. A jeep or a truck, maybe, but not a plane. (01:44:45)
Factual error: Just before Col. Stewart activates his equipment, we can see one of his men working with a welding torch on telecommunication equipment. You can't patch telco connections using a welder. (00:28:50)
Audio problem: In the climactic scene where the 747 is taking off, the general applies full power on the throttles and the engines spool up to full power as they should. However, in the next shot from the cockpit, the general is pulling back on the yoke, nobody's hands are on the throttles at all, and yet we hear a second (apparently) identical increase in engine power. Pulling back on the yoke has nothing at all to do with the engines - the noise we hear should remain at a constant level. (01:50:15)
Plot hole: At the beginning of the film, it is still daylight, which at Christmas, would mean it's about 4:30pm at the latest. The whole incident of the film lasts around 4 hours (figured by the scene when Barnes was talking to the planes and said the trouble started around 2 hours ago coupled with the fact that not long before that, Trudeau confimed that Holly's plane had only 90 minutes worth of fuel left). So why at the very end are there shots where it appears the the sun is rising in the distance? (And no, it's not caused by the fire of the exploded plane. By that reckoning, the terroists would have had to have taken over the airport well after midnight, which is pretty much impossible since Esperanza's plane was already on route.) (00:00:35)
Continuity mistake: During the last fight scene on the wing of the plane, just after the guy is sucked into the engine, general Stuart comes rushing out and yells something like "it's time for the main event". At this, John rolls over onto his back. The shot then switches to much further away, and he is still on his stomach. The camera cuts in close again, and John is back on his back, and sliding towards the center of the wing. The camera cuts away again and shows John back on his stomach and just now rolling over. (01:43:40)
Factual error: When we see pictures from the cockpit of the planes we can see the individual snowflakes. That is impossible with the speed an airplane is flying.
Continuity mistake: When McClane is desperately trying to get out of the manhole cover to avoid the plane, he props it open with a steel bar. Moments later, just before the plane runs over it, the bar is gone, so there should be nothing holding it open. The size of the gap between cover and runway also decreases between these shots. (01:14:50)
Revealing mistake: On one of the first shots of inside Holly's plane, you can see the blue screens through the windows. No, it's not blue sky, in all the following shots the sky outside is orange. (00:16:30)
Continuity mistake: The dead bodies of the SWAT team move around on the escalator between shots. The best example of this is after the last SWAT guy dies, there is a body or two near the end of the escalator. They disappear or at least move much further away after McClane drops his gun on the escalator. And all this happens while the escalator is not moving. (00:45:15 - 00:48:00)
Answer: In the first movie he's a New York cop visiting his wife. In the second Die Hard, he tells the airport officer that he's LAPD and moved there because of his wife's job. In the third Die Hard film, he most likely went back to New York because of marital problems and became a New York cop again.