Revealing mistake: In the scene where Axel throws the art dealer's henchman onto the buffet table, if you watch carefully (or use slow-mo) you can see the stunt double pulling off that manoeuvre. There is also a stunt double being thrown over the table.

Beverly Hills Cop (1984)
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Directed by: Martin Brest
Starring: Eddie Murphy, Judge Reinhold, Ronny Cox, Steven Berkoff, John Ashton, Lisa Eilbacher
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Detective Rosewood: Wow. You know, it says here that by the time the average American is fifty, he's got five pounds of undigested red meat in his bowels.
Sergeant Taggart: Why are you telling me this? What makes you think I have any interest in that at all?
Detective Rosewood: Well, you eat a lot of red meat.
Question: Did Eddie Murphy improvise his hotel meltdown speech (where he claims to be a reporter) or was it scripted?
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Chosen answer: Much of Axel Foley's lines were improvised, including this scene, according to the commentary. But many other actors improvised their lines too, most notably Bronson Pinchot. The script was originally written with the intent of Sylvester Stallone playing Axel and as such, the issue of his race wasn't scripted and the director tried to avoid mentioning race in the film. It was Eddie Murphy that would bring it up in improvised lines.
Bishop73