Audio problem: The guitarists weren't going with the sound of drumming on their guitars. Also the timing of their lips while singing were wrong.
Audio problem: When the kid shows El Mariachi how he plays, you can hear the part that he's not playing because it's a constant sound on one string and he's stroking all the strings at the same time.
Audio problem: When the bad guys in the car are shooting at Danny Trejo, the kid with the broken leg kills him with six shots we see and hear, but the slide on his gun locks back after 5.
Audio problem: Why didn't we hear the 18-wheeler come rolling down the street when the little boy was going to get El Mariachi to come with him to get his guitar? He crosses the street and then the sound appears and the truck appears.
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.