Continuity mistake: Throughout the show, the character's lockers continually change position. For example, Rachel's locker is at first near the end of a row, a few down from Quinn's, yet later it's in the middle of the row, nowhere near any of the other Glee kid's lockers, and even later it's the second one down in a completely different row.
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.
Deliberate 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.
Continuity mistake: In 3x14 (On My Way), Quinn apparently texted Rachel that she'd be there soon at 11:01PM on February 9, 2012. Quinn got Rachel's text back at 4:14PM. When we see Rachel's phone again, her text saying "HURRY!" is gone. (In addition, Feb. 9th 2012 was a Thursday, not a Saturday).
Factual error: After he gets fired from his teaching job, Mr. Ryerson makes a living reselling the medical marijuana he receives for depression. Ohio is not one of the 16 states (and District of Columbia) that have medical marijuana laws, and NONE of the states allow it for treatment of depression.
Deliberate mistake: During almost every scene that involves the main actors in the hallway or in a classroom with a window to the hallway, there are people passing by at random intervals. Even if the scene takes place in the middle of class or after school, there are random extras wandering the halls. In real life, unless they had about 15 minutes between each class and every single club met after school every single day, there wouldn't be that many people in the halls.