Revealing mistake: When El Mariachi's one friend first fires a rocket at the bad guy's limousine in the climactic battle, you can see that the rocket itself never explodes, despite the side of the car blowing up. The rocket simply lands next to the car, and then remains there in plain sight whilst the side of the car blows up, revealing that it is just a prop replica.
Revealing mistake: When Antonio Banderas runs over the guy at the end of the big shoot near the end of the movie, the guy getting run over has been replaced with a dummy. You can tell because of how easily it moves and how much it twists. You can also slow the film down to see that the dummy's plastic hand is visible.
Revealing mistake: In the fight scene in the Tarasco bar, one of the bad guys jumps on El Mariachi, but he stops him with his feet and pushes him off and shoots him as he is flying through the air. As the bad guy is shot, you can see the tape holding the squibs on his shirt.
Revealing mistake: When Antonio Banderas shoots the guy with the broken ankle at the beginning of the shoot-out on the roof near the end of the movie, he falls off. Slow-mo his fall and you'll see the air mat he's suppose to land on, it's a huge evenly raised lump in the sand about a foot high and surrounded by white rocks. He even sinks into it when he lands.
Answer: Tito Larriva as Tavo says (in reference to Steve Buscemi) that "This guy smells like shit." The name of the song being played is "Manifold de Amour" by Latin Playboys.