Other mistake: In the beginning of the episode the Chem teacher tells the principal he can't take over for the other teacher's 5th period because that's his only free period but T.J. later on during the trial says Mo probably left his playbook during 5th period. (00:03:17 - 00:12:26)
Factual error: In the scene where T.J. Is explaining the formula to Mo that is written on the board, the right side of the equation (x-1)^2 is wrong. It should be x^2 - 2x + 1, not x^2 - 2x - 1 when expanded. Also, at the start of the scene with the formula, the coach who is teaching the class states he wrote it, and then it is assumed T.J. came up and finished solving the equation, but the writing is exactly the same. (00:08:15)
Revealing mistake: When Yvette and Floyd are playing basketball, the guys come home and distract him. Yvette makes some impressive shots, and you can tell that it's a stunt double because the hair is totally different. Yvette's is big and puffy, and the double's is long and straight. (00:08:15 - 00:09:40)
Revealing mistake: A little oversight on the part of the producers. At the final scores that we are shown, Amy has $10,000, TJ has $9,800, and Travis has $2,400. This all adds up to $22,200. Even if they only answered $400 questions (which we can see that they don't), that's about 55 questions at best, only in the first half. That would run way longer, probably about three or four times as long, as any normal game show. And there's no mention of any other rules regarding the scores so there's no reason to think that there are bonus questions that could raise it that much.