Continuity mistake: In the shower scene, we see that in front of Carl, there is a man with brown hair and a moustache in front of him, but then when the shot changes, the man has moved cubicles and a man with white hair has taken his place, and he wasn't even in the previous shot.
Continuity mistake: In class, when Lisa is sitting at her desk, pondering the Jebadiah mystery, her tray of cookies and glass of milk is very visible. Then when Lisa says "The missing piece of the puzzle. I've got it." and runs out of class, the cookies and milk are no longer there.
Continuity mistake: Right at the beginning of the episode when all the children are on the bus we can see that in front of Nelson is Bart and behind him are Lewis, Martin and Wendall. Then when the shot changes to behind Nelson, Lewis has swapped places with Bart, Bart has disappeared and some weird kid is sitting where Lewis was.