Continuity mistake: When the lady sitting next to Holly pulls out her stun gun, her book is resting against her stomach. However, in the previous shot from a different angle, the book isn't seen.
Continuity mistake: In the airport lobby, when the two policemen come at the bar they have "snow" all over their clothes. In the next shot they are shown from behind sitting at the bar and Lorenzo's brother has no snow on his jacket. Seconds after Mc Clane comes to talk to them and the cop has snow on his shoulders again.
Continuity mistake: When McClane grabs Marvin the janitor and pushes him against the lockers, McClane's thumb changes position on the gun, some shots it's on the hammer, other shots it's around the handle.
Continuity mistake: When John and his wife hug, his hand suddenly appears on her head.
Continuity mistake: When Barnes and the SWAT team reach the Annex Skywalk, they get on the moving sidewalk. Before the terrorist stops the moving sidewalk by pressing the button, the sidewalk is already stopped, even though the light was still green at the time.
Continuity mistake: When the general exits the plane with Colonel Stuart, nobody shuts the door. It is closed in the very next shot.
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.