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 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)