Factual error: During the scene where Navajas is throwing knives at El Mariachi and then the Bucho gang in the limo, he slides down in front of the car. The license plate simply says "Mexico" under the serial. Actual Mexican plates of the time period in the movie use the official state abbreviation followed by MEX to identify the state of issue. For example, JAL MEX for Jalisco, which is where the JWF685 serial seen on the plate would have been issued.
Continuity mistake: When the knife throwing assassin is after El Mariachi, he throws the first knife at his left arm and the second one at his right hand. Then we see El Mariachi going around the corner, with most of his back out of view, as the assassin throws the third knife at him. A few moments later, we see El Mariachi taking the knife out of his back - it's right next to his shoulder, and it was impossible for the assassin to hit it from where he was.
Other mistake: In the bar fight/shoot out Antonio Banderas shoots a fan onto one of the gunmen and we see the man fall down face first into the camera with the fan on the back of his head, Antonio walks around the bar and guy is suddenly laying on his back and turned completely around with fan on his chest.
Continuity 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.
Continuity mistake: In the fighting scene with Antonio Banderas and his two guitar friends, before everybody starts shooting we see the little boy walking around strumming his guitar. In that first shot the strap is crossing the back of his neck. But in the very next shot of the boy, that rope is hanging down almost on his knees.
Continuity mistake: During the rooftop shootout Hayek has a red and a black shoe on. At one stage you see both shoes in her hands then there's a shot of Banderas and then its back to Hayek and she's taking the red shoe off again.
Other mistake: How does Banderas shoot the bad guys falling back off the building? It's impossible from the angle he's at.
Continuity mistake: When Bucho shoots at the limousine glass when it first arrives, the shot on the window changes around a couple of times.
Continuity mistake: After the boy gets his right leg broken by Christos in the fight scene at Bucho's villa:  The boy begins to stand up (straight, without turning his body). In the next (bad) cut his movement should be continued, but he suddenly is erecting in a 360°-turn finalized by jumping in the air to knock Christos down with his foot.  If you would look down at him from above the scene, his right leg would describe a clockwise movement towards Christo's face. Look sharp and you will see that it never reaches its aim because the distance between the two men is too long. Before the foot hits its aim another very bad cut is set. In this one his leg would describe a counterclockwise movement, not clockwise as the movement has begun the cut before. To accomplish the motion instructed by this cut, the boy would have had to stop his leg's movement abruptly in the middle of the foot-kick, when the foot has the highest speed and force. There he would have had to fling his foot back where it came from to finally knock Christos down. And all this without having any footing from the ground whilst his jump.