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.
Answer: The song is called "El Bimbo" and was performed by Jean-Marc Dompierre and his Orchestra. It's a cover version, the song was originally produced by Bimbo Jet (a French group). This song is played in several other Police Academy films.
Bishop73