Continuity mistake: In the scene where the Graboid is pulling the truck you can see that there is a gun rack and a gun in it. Right before they are about to hit the rock you can see that the gun falls off of the gun rack. The gun goes on and off the rack between the following shots. (00:30:25)
Continuity mistake: When the Graboid scares Earl and Grady into backing up the truck over the ridge and getting it stuck, the hill they stop on is empty - that is, no rocks. But later, there's a big rock right next to its right side that Grady jumps onto. Also; when the truck first crashes, the angle makes the windshield roughly level with the ground. But subsequent scenes show the truck at a different angle. (00:42:20 - 00:47:35)
Plot hole: When Earl, Grady, Burt and Kate are running from the truck that Burt shot, they go towards the cantina, which has a couple of smaller blue and white structures beside it. In a wide shot as they're running, we see the 1st shed at the side of the frame. A moment later Earl sees several walking Graboids in front of the 2nd shed. The beasts were in plain sight, yet nobody noticed until they were almost on top of them. (01:14:50)
Visible crew/equipment: When the Shriekers are trying to find Burt in the front loader (tractor with bucket) with their tongues, as the camera pans it catches the arm of a puppeteer controlling the tongue, in front of the front loader. (01:18:00)
Revealing mistake: It's very clear they blew up a model of the buildings. The grass seen just before the explosions is way too long and is not as long when the characters are running away. Further, the truck and the barrels have disappeared at the explosion shot.
Continuity mistake: In one of the first scenes when Grady and Earl are riding to the oil site, Grady attempts to take the last soda. If you watch Grady closely when Earl tries to play Rock, Scissors, Paper at first he is holding up his right hand, then it goes to Earl, then it goes back to Grady holding up his left hand.
Revealing mistake: When Grady & Earl blow up their first graboid, one of the pieces of orange goo that hits the truck flies in from the LEFT. All the other pieces of orange goo get flung in from the right.
Audio problem: There is a scene just after Earl and the new guy arrive at their base, when a truck (driven by one of the Mexicans I think) pulls up from the left hand side of the shot. If you listen you can only hear the truck's engine from when it comes into shot. This suggests that it was waiting just off shot and then drove in, rather than coming from any distance as you would have heard it approach.
Continuity mistake: Just before Earl gets sprayed with the fire extinguisher, he wraps a shirt around his hand. When he takes the shirt, you see he has no gloves on. Then when he asks for gloves the camera cuts to a different angle and the gloves are on him, even though he never even took them off the other guy.
Continuity mistake: In the scene when Grady says "son of a..." when the Graboid is dragging the truck, there is a shot of the truck driving forward.
Continuity mistake: After Burt gives the double rifle to Grady he closes the box he got the rifle from. Over the next shots the box changes from being closed to open and closed again two times as the shot changes.
Factual error: As Burt is driving, he is producing a video diary. He indicates it is 1900 hours (7PM) on May 14th, and yet it is pitch black outside. Nowhere in Mexico would the sun have set by 7pm in May.
Continuity mistake: At the end where the building explodes, everyone stands up from the pit. Burt is standing up in one shot, but in the next, he is kneeling down.
Visible crew/equipment: In the shot where the camera examines the hole in the wall and car made by Burt shooting the shrieker. You can see the shadow of the cameraman on the wall and his reflection on the car (near the top right corner).