Signs on a chain-link fence and in the model town state that the area is managed by the U.S. Department of Energy, which was not established until October 1977. In fact, the U.S. stopped atmospheric tests of nuclear weapons in 1962, when the area would have been managed by the Department of Defense.
When Bobby is lying down in the trailer, he checks his watch at 11:49 PM and the gun can be seen behind him perfectly parallel with the ledge. He then hears Beast barking outside, gets up and reaches to grab the gun. The camera cuts to a close-up of the gun as Bobby grabs it, however it is now rotated 45 degrees between shots.
When all of the family except dad is in the trailer on the first night Bobby locks the door from the inside with a key. After the Doug and Lynn say that they are going to sleep in the truck because it is too crowded they walk right out the door without unlocking it.
In the beginning when Pluto kills the first researcher, you see
the ax go through the mask, so the mask has a hole in it. When the researcher falls on the ground, his mask doesn't have a hole, it's just like it was.
When Beauty runs into the gas station and Lynn goes after him,
Lynn sees the bag on the table, the one with the ear inside it, then lifts a flap to peek inside the bag. The flap then falls down just the way it was, closing the bag again. When the gas station owner looks at the bag just after Beauty and Lynn left, the bag is wide open.
The first time we see the family's 1990 Chevy Suburban, it's sitting on tall/wide off road tires and after-market chrome spoke wheels. Later in the same scene and for the rest of the movie, the Suburban is riding on the more narrow factory stock wheels and tires .
When Doug is in the town in search for Catherine he reaches the house with the machine chugging next to it. Here the sunlight is coming from the right side of the house. In the next shot, the mutant with the neck brace drags a body from in front of the house. Now it can be clearly seen that the sun has moved all the way to the left of the house.
When Doug takes Beast through the tunnel, he's carrying the torch in his right hand and the baseball bat in his left. When the shot cuts by 180 degrees as he comes out into the light, he has the bat in his right hand and the torch is nowhere to be seen (he could have just dropped it in his bag, but there certainly wasn't time to switch hands with the bat).
Lynn hits Lizard on the left side of his face/head with the skillet. During the next few quick shots, Lizard screams and is pointing the gun at the baby, and there's no blood on the left side of his face. Once Lynn says "no please", the camera view of Lizard from behind Lynn shows blood all over his left cheek. He then reaches out to touch Lynn's face, we see a shot of Lynn's face, then when it cuts back to Lizard the blood on his left cheek is gone.
When the family is setting up the camper after they crash, the shadow on the wall of the camper from the shade cloth is not matched with the time. It starts with the sun very high in the sky and then it shows the shadow like the sun is very low, all within a few minutes of conversation.
When Doug enters the house and takes the baby, Big Momma is watching Divorce Court. The picture is crystal clear. There was certainly no cable in this area, and a broadcast signal, if it could even be picked up, would likely be of extremely poor quality due to the mountains. These mountains also block the family's radio transmissions.
The fire extinguisher used to attempt to put out the fire on the father is a CO2 (carbon dioxide) type. The man using it was holding on the nozzle, but anyone holding on to a CO2 nozzle would have their hand severely frozen and stuck to the nozzle.
The goof items below may give away important plot points.
In one scene where Doug is battling Pluto in the house, Pluto takes the ax to Doug's fingers, chopping off the tips of them. Later in the movie, both Doug's left and right hands are fine, with no fingers cut off.
At the end when Doug is chasing Ruby because she has Catherine, Lizard shows up. When Doug is fighting Lizard, he hits Lizard in the nose with the shotgun and breaks his nose, blood is seen all over Lizards shirt, but when it switches back to Lizard about 2 seconds after, you see all the blood is gone off of Lizards face and shirt.
Near the end, Bobby closes and booby-trap's the trailer doors. After he and his sister have tied an attacking mutants hands to a side trailer window, they climb out the back window and run up a hill. When they look back at the trailer the door is now wide open. Next, the mutant frees himself and we see him open the, now closed, trailer doors setting off the booby-trap.
At the end of the movie, Doug has Beast by his collar, in that scene you can see the dog struggling like he doesn't want to be still, in the next scene (different view) Beast is calm and standing beside him.