The Scrabble board keeps changing.
The whole family goes to the opera to see "Carmen". They have balcony seats and the stage is to their left, yet later on you can see them looking to their right.
During the "Kwyjibo" scene, Homer is seen holding a brown skinned banana in his left hand. The banana remains in his hand through the scene when Bart is forced to explain what a "Kwyjibo" is, but when Homer begins to chase Bart, the banana disappears completely with no sign it was ever there.
Homer thinks that Albert Einstein invented the light bulb, but in The Wizard of Evergreen Terrace (1998) it's implied that he does in fact know that it was Thomas Edison.
In the Scrabble game at the beginning, Marge plays HI and says that this scores two points. In fact, H is a four-point tile, so HI would score at least five points.
Bart's IQ test is referred to by Marge and Dr. Pryor as an aptitude test, which is instead used to determine the type of work you're best suited for.
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