Eddie Murphy, John Ashton, and Judge Reinhold improvised most of their comic lines. Literally hundreds of takes were ruined by cast members, actors or the director laughing during shooting. During the "super-cops" monologue, Ashton is pinching his face hard and looking down in apparent frustration. He is actually laughing. Reinhold put his hand in his pocket and pinched his thigh really hard, trying to prevent himself from laughing.
Axel Foley's T-shirt is from Mumford, a real-life Detroit-area school one of the filmmakers attended. When the film came out, the school got orders for the shirts from customers all over the world.
To cast the roles of Rosewood and Taggart, the director paired up various finalists and asked them to do some improvisation to get a feel for their chemistry. He paired up Judge Reinhold and John Ashton and gave them the following direction: "You are a middle-aged couple, married for years. You are having a conversation on an average evening." Reinhold immediately picked up a nearby magazine and the two improvised the "five pounds of red meat in his bowels" bit almost exactly as it eventually appeared in the movie.
Eddie Murphy became very tired while filming the police station sequences. The crew offered him coffee, but he refused to drink it because he refuses to take drugs of any kind. Eventually he relented and took small sips of coffee to stay awake. He became very energized and ad-libbed the "super-cops" monologue.
Originally two men were supposed to be working in the art gallery scenes. When the director heard Bronson Pinchot's Serge impersonation, he thought it was so hysterical that he scaled back the other part to give Pinchot more screen time. The second actor shows up briefly, with his shirt collar open too wide, and Serge comments on it.