Continuity mistake: While Bart starts the I.Q. quiz and is reading it out loud, his teacher says "Shh. Visualize it Bart." While this happens if you look in the background you can see the alphabet line. It starts out Tt Uu Vv Ww, then Bart's teacher blocks out some, then you see the letter T again. (00:04:50)
Continuity mistake: At lunch, two boys exchange Bart's sandwich for a grape. When they give him the grape, it lands in Bart's right hand but in the next shot he has it in his left hand, and when one boy gives Bart a cup, the grape is back in his right hand again, and in the shot after that, the two items have changed positions.
Continuity mistake: When Homer grabs hold of Bart's arm and demands to know what a "Kwyjibo" is, he is holding a brown skinned banana in his left hand. The banana remains in his hand when Bart is forced to explain what a "Kwyjibo" is, but when Homer begins to chase Bart, the banana has gone. (00:03:10)