In one of the previous drafts written for Sylvester Stallone, Billy Rosewood was called "Siddons" and was killed off half-way through the script during one of the action scenes deemed "too expensive" for Paramount to produce. Only after Martin Brest cast Judge Reinhold and John Ashton was the decision made to keep Rosewood alive due to his chemistry with Taggart.
The song which plays during the strip club scene is "Nasty Girl", by Vanity, and was recommended by the real-life stripper who was hired for the scene.
In the shootout when Axel, Taggart and Rosewood are trying to get to Victor there is a sequence when the three of them are shooting over the top of a short wall. During this sequence all three fire at once, as Axel fires the slide of his gun goes back indicating he has run out of ammunition. The next shot shows them all firing again and only after this is Axel shown reloading.
Towards the end of the movie, when Foley shoots Zak in Maitland's mansion, we see Jonathan Banks (who plays Zak) lying on the floor. In the next shot, his stunt double is seen lying on the floor.
Axel Foley: You can't go in 'cause you're a cop in this town. You go in there without probable cause, they're gonna call it an illegal search. You know that. Or didn't they teach you that in cop school?