Continuity mistake: At the start when Billy Ray (Murphy) is backing away from the cops after he was pretending to be a cripple, he passes the Heritage club. In front of the steps of the Club, he turns to face the other way. The camera changes angle as Billy Ray completes his 180 turn, but he is now no longer at the steps of the Heritage club, but about 10 feet beyond it, nearer to where the other cops in the patrol car come out of the alley way.
Continuity mistake: When Valentine (Murphy) and Winthorpe (Aykroyd) are at Winthorpe's house at the end of the movie. Winthorpe is on the floor cleaning his gun. In the next shot Ophelia (Jamie Lee Curtis) points out Beeks on TV and Valentine and Winthorpe jump up from the couch when Winthorpe should have been and was on the floor.
Continuity mistake: When Valentine is in the limousine with Mortimer and Randolph, he has a bunch of cigars in his left hand. The position of those cigars change from shot-to-shot. One is hanging down very low when looked at from Randolph's side of the car, then immediately it is even with the others when seen from Mortimer's side.
Deliberate mistake: Eddie Murphy is giving his first party and tells everyone to leave. The valet holds all the coats in a perfect pile for the people to grab them as they leave. Although everyone rushes out of the party, it's very strange that the first person to leave takes the first coat, the second person the second coat and so on until the very last guest. No one stops to check if the coat they're taking is really theirs. (I guess it was shot this way to keep the good pace of the sequence).
Factual error: When Beeks is locked in the cage with the gorilla, it reacts in an overtly aggressive and sexual manner. First, gorillas are shy and gentle creatures. The male gorilla would be scared of him, not the other way around. Second, gorillas identify each other by their smell, and the smell of a female in heat is very specific. Beeks would smell like a horsehair rug and the male gorilla wouldn't be the slightest bit interested.
Continuity mistake: When Eddie Murphy and Dan Aykroyd's vehicles pull up next to each other in traffic, Eddie's window as seen from the outside is fully open, with a small closed side window. When we cut inside Eddie's limo, the full window is completely closed and there's no side window at all. It's a completely different limo.
Visible crew/equipment: As Murphy and Aykroyd are leaving the bathroom to head to the trading floor, you can see the shadow of the dolly track on the lower right hand side of the frame. For a brief second you can also see the actual dolly track before they enter onto the trading floor.