Other mistake: When the kids are opening their lockers, they enter the code, then pull on the lock to open the locker. The closed lock is still attached to the front of the locker. When they close it, it's magically locked again without them ever opening or closing the lock. In reality, these locks would be useless, or the locker doors wouldn't open.
Other mistake: Many of the Warblers appear in McKinley throughout the show, even after the Warblers were introduced. An example of this is that Trent is often seen walking throughout the halls of McKinley. He even sits in front of Finn in "Substitute" when Holly Holiday is teaching the students Spanish.