Revealing mistake: You can see it's a stuntman and not the Zack actor rolling over the buffet at the Harrow's Club.
Continuity mistake: During the opening chase, the truck's under-bumper license plates vanish in some shots, usually the same shots that show a wood board protecting the grille.
Continuity mistake: When Axel goes to talk to Jenny he asks her if there is somewhere they can talk and you see his left hand start to rub his stomach, but when the camera angle changes his hand is now in his back pocket.
Revealing mistake: When Axel shoots Zack, Maitland's chief thug, Zack stumbles backwards. As he does, he turns his head to watch whether he's stumbling back the correct way (if it had been a result of the bullet impact, his entire body would spin around).
Continuity mistake: When Axel goes to talk to Victor the first time, the pen on Victor's desk changes from being in the horizontal position to vertical between camera angles. One in the pen holder moves as well.
Other mistake: The bit part actor who plays one of Rosewood and Taggart's colleagues on the force is credited as "Owensby" on his desk sign (in the scene where Bogomil is asking where everybody is) and as "Owenby" on the end credits.
Factual error: When Axel and Taggart are taken under fire by the gunner with the dark glasses (who is shot by Billy), notice that the gunner stands perpendicular (i.e. at a 90° angle) to the stairs where Axel and Taggart take cover. Yet, two of the bullet holes appear in a column at the base of the stairs which would have come from a different trajectory, namely in line with the stairway and thus from Axel and Taggart's flank.
Continuity mistake: When Axel and Jenny pull up to the Bonded warehouse, you see Axel's arm resting on the passenger door but when the camera angle changes his arm is inside the car.
Continuity mistake: When Maitlands guys remove the bonds from the box, they have opened the lid and 4 nails are sticking out. But they don't hammer them back in. Nevertheless the nails disappear from one shot to the next.
Continuity mistake: When Axel is booking into the Beverly hills hotel the clerk and the manager change from standing very close to each other, to very far apart, depending on the different camera angle.
Continuity mistake: When Axel is telling Bogomil what he's really doing in Beverly Hills, you see Bogomil's hands in the front of him as he is talking but when the camera angle changes only one hand is in front and the other is to his side. Happens about 3 times during the scene.
Visible crew/equipment: During the truck chase scene in the beginning, three cop cars slide into parked cars as they turn following the truck. In the middle car, right between the driver and the passenger, is a full camera rig. Next shot it's gone.
Continuity mistake: When Axel and Mikey are playing pool, the guy Axel is playing calls out his shot and you see about 3 balls on the table not including the cue ball. Mikey bets the guy that he can't make the shot and you now see only the 8 ball on the table.
Continuity mistake: When the police pull up to the back of the semi, Axel was holding the money in his hands to his side but as the camera angle changes he's now holding the money up in the air.
Continuity mistake: When Axel is talking his way into the club to see Victor, right before he's allowed to see Victor the camera angle from the back shows him rubbing the back of his head with his left hand but the camera angle from the front shows his hand at his sides.
Continuity mistake: When Axel and Jenny go to Victor's warehouse you see Axel walk up to a crate and put both of his hands on it. The camera angle changes and his hands are no longer on the crate and he's pointing to a label on the crate telling Jenny that this is what they are looking for.
Continuity mistake: When Inspector Todd is yelling at Foley you see Jeffrey standing right behind Axel looking at the lockers, and when the camera angle changes he's now looking right at Axel.
Continuity mistake: When Axel and Mikey are at the bar Mikey puts his hand on Axel's neck. The shot changes and the hand is now on Axel's shoulder. The shot changes again and the hand is missing.
Audio problem: Taggart and Rosewood try to pursue Foley from the hotel but their car stalls from the "banana in the tailpipe", and when Rosewood tries to restart it, it makes the starting sound of an older Chrysler, when the car is actually a Mercury.
Continuity mistake: When Axel shoots Zack at the mansion, he falls to the floor, dead. It cuts to Axel, and then back to Zack, whose position on the floor has changed a little bit. The white piece of wood that he fell on is gone too. Also, I can't be too sure about this, but it does look to be a different actor.
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