Continuity mistake: When Billy's Principal is introducing him to his class on his first day of school, Billy's name is already written on the blackboard behind him. There is a shot of the class saying 'hello' to him and when the camera returns to Billy, the blackboard is clean and his Principal asks him to write his name on the board.
Continuity mistake: On Billy's second day of school, in the first shot of the teacher at the board she writes something like "long division - (a bunch of numbers) 5 (divided by symbol)". But a few shots later, when it shows her again, the writing on the board only says "long division". Half of her writing has been erased.