Visible crew/equipment: When Frank is listening to the alien leader and realizes the entire town is stuffed into the boxes, he goes back to the rest of the guys. When he closes the door, the shadow of the camera man is visible on the door. Shadows from crew members are visible in this same room several times.
Revealing mistake: When the collector gets into his car, he tries to close the car window. Robert puts his hand through the window. The collector manages to close it well enough to trap Robert's hand and takes off in his car. From a camera view outside the car, you can see the window isn't closed enough for Robert's hand to be trapped.
Continuity mistake: In the start of the film you see "the boys" driving in their car talking on a C.B. to another man in the group they are meeting. If you notice the one doing the talking spends most of the time with the CB backwards using the mounting notch by his face, but when the scene switches from inside the car to outside it is turned around the correct way.
Revealing mistake: When Barry has shot the alien in the head at the beach the camera is filming the aliens feet as the blood starts dripping. Then the camera start moving up and when the camera reach the alien's waist level you can see a sudden cut. This is done so the fake alien puppy with half its head gone can be used.