Continuity mistake: When Elliott gets food for himself and ET he takes the milk container from the top shelf of the fridge, and we see an empty space beside the Skippy peanut butter where the milk had been, but after Elliott drops everything onto the floor, in his next two closeups note the milk container (it has a distinctive curved design) is back on the shelf in the same spot beside the Skippy jar.
Continuity mistake: When Mike is trying to get Mark to ask Stacey out, there is a shot of her behind the counter and Stacey's hair is pulled back on the sides in french braids with ribbons on the ends. Then when Mark approaches Stacey, her hair is pulled back in a clip. The first shot of Stacey with the braid, is actually cut from a scene later in the film, when Mark and Stacey talk at the counter. (00:27:35 - 00:28:20)
Continuity mistake: Paul Kersey boards a bus where the line number reads 990. When he gets off, the number is 99. He could not have changed buses because the number of the bus itself remains 8027 throughout. (00:54:50)
Continuity mistake: When Nicodemus is telling Mrs. Brisby that he looked at the words under the latch on the door and understood them, there is a clear, large label under the door. Then a different angle is shown and there is no label on any of the doors, but you should be able to see it still. (00:52:25)
Revealing mistake: When Reggie and Jack are following the Porsche they're replaced by obvious stunts. Eddie Murphy is a heavier and older man with an afro hair, for example.
Continuity mistake: Dining at the Chinese restaurant, Rita asks a fresh refill of her drink. Throughout the scene, the glass appears in her hand seemingly at random between cuts. Not just that; the level of liquid changes as well. It is particularly obvious when she says that the mystery autograph looks like signed by "a retard." (00:17:00)
Character mistake: The news article on the murdered gentleman David Carradine discusses has the word existence spelled wrongly. It says existance. (00:37:57)