Revealing mistake: When Robert and Julie are attacked by snakes outside the cave, notice that in the shots when you see the backs of Robert and Julie there are hardly any snakes on the ground (I counted one) compared to other shots. The shots of Robert's leg as he sweeps the snakes away are almost certainly of a snake handler instead of the actor.
Revealing mistake: When Ham drives the van through the road barrier, the pieces fall off very easily considering how slowly he was travelling. In the next shot it is shown that the remaining barrier sections are both split vertically, revealing that they were sawed in the same direction beforehand, then the 'broken' pieces loosely affixed before the collision.
Revealing mistake: When Julie is almost converted, a fake Donovan bursts in and starts firing a blaster rifle. Look closely at the first shot: the rifle is held way too high, so the shot should have gone into the ceiling; yet the blast goes straight forward.
Revealing mistake: The two Elizabeths are both played by the same actress, except in the shots where both are seen together. Continuity mistakes in the second Elizabeth's death scene reveal this, such as the second Elizabeth's head position changing, and the first Elizabeth's jacket being open/closed between shots.
Revealing mistake: When the two wildcats throw hand grenades at the Visitors, the grenades are obviously fake because the explosions do not occur at the same place as where the grenades land. The detonations have obviously been located in a safe place away from the actors.