Other mistake: What Lucas supposedly did to one of his teachers at his previous high school (Paul Garrett at Milton High School in San Francisco) is far-fetched. Paul told Mr. Butler that Lucas also blackmailed him for an 'A' by videotaping him in his house drinking alcohol with an old friend. Lucas hunted down Paul's old friend (how would Lucas know about this friend?) and paid him to get Paul - a recovering alcoholic - to start drinking again (how would Lucas know that his teacher was an alcoholic, eight years sober?). Moreover, it doesn't make sense that someone's old friend would accept money from a teenager to get his eight-years-sober friend to drink. Lucas may be clever and conniving, but he was still a kid - someone educated adults should be able to outsmart... or at least not get duped by him.
Other mistake: Mr. Butler told Principal Fermont that he'd like to talk to Mr. Ward about Lucas, and she gave Mr. Butler Lucas' home address. Mr. Butler went to Lucas' home without notice more than once and even went upstairs into Lucas' bedroom after Mr. Ward - a lawyer - told him to leave. If a teacher wants to talk to a student's parent, the parent would be asked to come to the school for a conference.
Other mistake: The grade report that Lucas received in the mail indicated that they were "Final Grades" (Sixth Cycle). When Detective Speck asked Lucas why he thought Mr. Butler believed he "had it out for him", Lucas responded that he was trying to figure that out but it had been "ever since he gave me an 'F' on my midterm report card." Also, now that instructors in many/most (all?) schools submit grades on-line, students are able to view their grades on-line and hard copies of report cards may no longer be sent to students or parents via USPS. (00:51:15 - 01:03:38)
Other mistake: The courses on Lucas' grade report are not given numbers or specific titles that would distinguish them from other courses (and levels) within a department. They are listed in general categories: "American History" (a minor distinction), "Calculus", "Chemistry", "English", and "French." A cover page for one of Lucas' assignments shows he was enrolled in "English 301" - still no descriptive title, but at least discernible from "English 101" and "English 201." (00:23:00 - 00:51:54)
Other mistake: Mr. Butler was late getting to his first period English class the morning he had a flat tire (which Lucas slashed). He went directly into his classroom from the door that opens to the outside of the building (which is odd for a school classroom). Typically, teachers must sign in as "present" and have a homeroom period before their first class. Someone would have had to cover Mr. Butler's homeroom and someone (perhaps Principal Fermont) would have gone to his first period class until he arrived. (00:28:35)
Other mistake: Mr. Butler is in Lucas' bedroom, finds a small (4"?) camera, and plays the part where Lucas is setting it up in the classroom to (hopefully) film Becca putting moves on Mr. Butler. Mr. Ward (Lucas' father) is standing in the doorway several feet away and cannot possibly see what is on the small screen, but asks if the girl on the tape is the one who died. (01:07:25)