Character mistake: It is highly unlikely that the recipient of Mr. Butler's application for the professorship position would not only call him so soon, but ask him to come to her office right away (where she would humiliate him for the things he wrote in his essay on "qualities that make me a good teacher"). Moreover, her failure to listen to Mr. Butler and give due consideration to his assertion that someone else actually wrote those offensive things showed poor judgment, especially since she knew the person who referred Mr. Butler and spoke highly of him. Someone tampering with his application would make more sense than believing that Mr. Butler actually wrote those things that criticized the very college he was applying to and boasted so much about himself. That Mr. Butler was not able to say more to make his point believable is also problematic. He is an English teacher, so should have the vocabulary and mastering of techniques to make a convincing argument, but he failed to defend himself.
Character mistake: Mr. Butler leaves his briefcase (containing his laptop) in his unlocked classroom during lunchtime. There's no rational reason to not take his briefcase with him to the teacher's lounge beyond furthering the plot.
Character mistake: In Principal Fremont's office, Lucas was asked why Mr. Butler thought that he "had it out for him in some way." Lucas responded that he was trying to figure that out himself and added Mr. Butler gave him an "F" even though all of his assignments were "A's." Principal Fremont replied, "Lucas, I don't want you to worry about your grade, okay? I will personally see to it that you get the "A" you deserve." This is not something a principal would say to a student, or say without first checking with his teacher to verify his grades and ascertain if there was a legitimate reason for issuing the "F." (01:03:50)
Character mistake: After Mr. Butler was late getting to his first period English class (due to having a flat tire), he picked up a few markers to write on the white board, but none of the markers had any ink in them. Mr. Butler then told the class, "Let's have a reading day." Public school teachers have daily lesson plans to follow, and a "reading day" would not meet his teaching obligation or fulfill his responsibility. (00:29:30)