Factual error: When McClane is trapped in the cockpit of Esperanza's plane, and the terrorists throw grenades in, it sure takes them a long time to explode, almost 30 seconds before he ejects from the plane and the grenades go off. Normal grenades have about a 5 second fuse. With a delay that long he could even have thrown them all back out at the bad guys.
Factual error: After recovering a pistol from a slain baddie, John McClane explains to airport security that it's a "Glock 7" (in actuality a Glock 17) and says that it's made of porcelain that makes it "undetectable by X-ray." Excusing the fact that not only Glock, but no major firearms company has ever mass-produced such a weapon due to functionality issues, it doesn't change that the ammunition would still be visible on X-ray. The armorer for the production team pointed these facts out on set and tried to convince them to change this detail, but they filmed it with these mistakes anyway.
Factual error: At the end when John lights the fuel with a lighter, this isn't possible with Jet A-1 which is what the Boeing 747 is fuelled with. This type of fuel is extremely hard to light. Even if you drop a match into a bowl of jet A-1, it will not ignite. Jet A-1 has to be compressed or have its temperature raised to a minimum of 38c/100f in order to ignite (which the compressing also does) so fuel in snow would never ignite in the way shown.
Factual error: Several runway numbers are mentioned in the movie: runway 10, 15, 25 right and 25 left. Runway 25 means course 250. The opposite end would then be Runway 7 (course 70). It would be unusual for an airport to have runways running course 70, 100 and 150, as that is way too close. And Dulles certainly does not. In the church occupied by the terrorists, the radar display (the upright one with the circular LED pattern, not a scope) shows the runway configuration of Las Vegas McCarran airport, not that of Washington Dulles airport. McCarran does have runways 25R and 25L, which are mentioned in the film.
Factual error: You cannot fire 'blanks' and 'live' ammunition from the same weapon without fitting a BFA (blank firing attachment). When a live round is fired, the bullet moving up the barrel seals the barrel. The exploding gas pushes in two directions. One - forcing the bullet out the end and two - pushing the working parts back. The working parts then move forward and pick up a new round. The BFA seals the top of the barrel, as a live round would do. If a live round is fired through a BFA you would be lucky not to blow the barrel.
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.
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.
Factual error: There is absolutely no way that Bruce Willis could have stood in the middle of an airport landing zone trying to keep the plane from crashing into the ground. He has no protective ear equipment on - that noise most definitely would have blown his eardrums out and blew him several yards away physically when it flew over him.
Factual error: The first shot of the church is a high up shot which pans down as the van enters the shot. High mountains can be seen in the background. The film is set in Washington D.C. (Note: the film was shot in the Denver area.).
Factual error: There is no Glock 7, and Glocks are produced in Austria, not Germany.
Factual error: In the tower, Leslie Barnes and a few men are talking about the Annex Skywalk, mentioning that it is a "VHF System." Barnes says the planes are so close it won't matter. VHF, or Very High Frequency, transmits far distances, hence why it is used by airports around the world. He should have said "UHF", which transmits shorter distances, as that would make more sense.
Factual error: A dangerous prisoner like Esperanza would not be flown into a civilian airport. He would be transported to the nearest USAF base, in this case Andrews Air Force base, always assuming that he is being extradited to Washington D.C.
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.