Factual error: At the end when Ms. Finster tells Randall to give her the names of the kids involved with the ball incident, she says to list them in alphabetical order. The first name Randall says is "Dettweiler, T.J." But "Blumberg, Mikey" would actually come before that, and given what we know of Randall, this isn't the kind of mistake he is likely to make.
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)