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)
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.
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.
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.
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: 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: 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: 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.
Continuity mistake: The scene where Fred is trying to rope the ostrich he gets pulled for a couple of feet and looks up at the bird. If you notice his shirt is dirty from being pulled by the bird. When he gets up to meet the taxi his shirt is magically clean.
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).
Other mistake: When Kate is introduced by Senor Ortega, she is introduced as Kate Riley, but the credits list her as Kate White.
Continuity mistake: When Earl enters the barn after being hosed down with CO2, the amount of vapor as he warms up varies from shot to shot with it almost not appearing to it heaving pouring off his clothes.
Visible crew/equipment: When Bert is hiding in the tractor bucket you can see someone waving around the tongue of the monster. (01:19:27)
Visible crew/equipment: When the Shriekers are trying to find Burt in the front loader with their tongues, as the camera pans it catches the arm of a puppet actor in front of the front loader controlling the tongue. (01:18:00)
Factual error: After Grady and Earl wreck their truck, Burt, Earl and Grady have a radio conversation. At one point Grady interrupts Burt's transmission cutting off his voice, but making it appear Burt can hear him. It's not possible to interrupt a transmission while the other person is also transmitting even though they're using repeaters which is why Burt's voice was cut off in mid sentence. The only way you can transmit and receive at the same time is if you're using full duplex. Burt's voice was cut off, therefore they are not using full duplex.