Continuity mistake: At the start of the film, Mahoney is wearing a white shirt with badges on it from the company he works for. When he's being interrogated by Sgt. Reed the shirt remains the same until the last part of the scene. The camera stays on Mahoney and we can see that the badges on the shirt are gone. If you look closely, you will notice that he is even wearing a completely different white shirt, which now looks more scruffy and creased.
Revealing mistake: When Mahoney first meets Larvelle Jones at the police precinct, Jones demonstrates his vocal imitation skills by simulating machine gun fire. In the shot with the unwitting crowd, look at the police man to the far left talking to the lady with the hat. That officer ducks down a split second before Jones lets loose with his gunfire sound.
Continuity mistake: When Mahoney first meets Jonsey, his (Jones') hands are cuffed behind him. Then he demonstrates why he's there in the station. His left hand has the cuff on. Then it's behind him again. Then, as he goes to mime playing a harmonica after Mahoney is led away, he rubs his right wrist as if it were cuffed the whole time.
Revealing mistake: When the lady is jumping over the fences, you can see that it is a man with make-up and a really ugly wig.
Revealing mistake: The wall that Hooks has trouble climbing over on the assault course flexes as she tries to climb it, indicating that it is really a piece of thin board.
Other mistake: In the scene where Hightower flips over the police car, if you look carefully after the car is flipped you will notice the car has no engine. Thereby making it easier to completely flip over than a car with an engine.
Other mistake: When Hooks runs over Copeland's toes with the squad car, you can clearly see that he is standing a good distance away from the car. I'd say that he would have had to have feet half a meter long for that be possible. The car also bumps up and down to signify that his feet have been run over. The car bumps too late though, and the front wheels have well passed Copeland before he moves to show pain.