Revealing mistake: At the end, though Williams is shot multiple times (by several rifles, no less), there's not a drop of blood on him and no holes in his clothes. Also, his "corpse" is visibly breathing. He's clearly meant to be dead, so the fact that he's an alien with healing powers does not explain why he's still breathing - or why the bullets left no holes or blood on his clothes.
Revealing mistake: Make-up for the space aliens was apparently changed after the closing scene in the store was shot and before any footage of the aliens' "true appearance" was actually taken. This resulted in Frisby, who is now telling the truth and finding no one to believe him, saying that the aliens had a single eye in their foreheads, when in fact, the aliens each had two eyes, in the traditional location.