Plot hole: It seems highly unlikely that Lucas would be able to "mess with" Mr. Butler's application for a professorship position, or be able to accomplish what he did in such a short amount time. Off-screen, Lucas went into Mr. Butler's briefcase (foolishly left on his desk in the classroom during lunchtime) and (correctly) assumed Mr. Butler's application was on his laptop. Lucas would have to be able to figure out Mr. Butler's password (something that could take forever), find the right file on his laptop, read or scan the application to determine what he could do to mess it up, write a new answer for "qualities that make me a good teacher", and leave the classroom before anyone saw him. Lucas would also have to assume that Mr. Butler would not notice the change when he printed the application, made a photocopy, and double-checked the application before inserting it in the envelope and mailing it.
Plot hole: Henry gave Principal Wilder reasons he believed Christina was being abused: "Bruises, exhaustion, decreasing school performance." When Susan confronted Glenn near the treehouse, she said, "I know what you've done. Emergency room visits, school absences, bruises..." Neither had any concrete evidence/proof. Emergency room visits should have resulted in detection or suspicion of abuse if that's what doctors or nurses believed, and they are among the mandatory reporters. Maybe Henry was wrong. (00:20:35 - 01:30:30)
Plot hole: Derek, who escaped the mental hospital by pretending to be his twin brother Tyler, was able to locate Tyler's vehicle by using the keys to beep its horn. Once inside the SUV, he apparently found Tyler's cell phone, which is odd because most people carry their cell phones with them. But Derek did not ask Tyler for his cell phone's password before rendering him unconscious - so how did he gain access to the cell phone without the password? (It isn't likely that Tyler previously gave it to him). (00:20:40)
Suggested correction: Tyler never left his cell phone in the car. He had with him when visiting Derek. We see him pull out his cell phone to show Derek a picture, so the phone was already unlocked, assuming he locks it with a password in the first place.
I haven't had time to finish posting the rest of the mistakes I have, but I just uploaded two that should show up under "pending submissions." They probably should have been posted before the one above. I suppose the real question is where the cell phone came from each time.