In the Mighty Mites opening game, Beaver is on the kickoff team waving at his dad instead of paying attention when the ball is kicked. But with 38 seconds left in the game, the coach says "Okay, the rules say I gotta play everyone" and he puts in Beaver.
When Beaver bring's the coach's play in and out of the huddle at the football game, his helmet chinstrap goes from buckled to unbuckled and buckled again on the close up and wide shots.
Towards the end of the film when The Beaver is up in his bedroom polishing his bike Wally walks in and there is nothing on his bedroom door. A few seconds later when his parents walk in the is a large framed newspaper article hanging on the door.
When Larry and Beaver are eating cookies at a café, Larry asks Beaver if he wants the cookies. Larry picks them up, but when they leave, the cookies are back on the table.