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.
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.