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 was having headaches and blurred vision, which he attributed to stress. He told the doctor he never considered a brain tumor. Henry started planning how to protect Christina but a sudden severe seizure was an emergency that resulted in surgery and hospitalization; Henry never returned home, but was writing in his red book at the hospital. The tape recorder with step-by-step instructions for his mother was in the safe - if he didn't know he was gravely ill, he wouldn't have prepared it.
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.