Deliberate mistake: Many times throughout the show, a large bandage or makeup blot is visible on Lea Michele's right wrist, which is used to cover up her "I Believe" tattoo. This is most visible during "Don't Rain On My Parade" and her "Poker Face" and "For Good" duets.
Intermediate Documentary Filmmaking - S2-E16
Deliberate mistake: This episode is meant to be entirely a documentary made by Abed. At the end of the episode, there's a shot where the gang is looking into Pierce's window, except the camera is right in front of the window they're looking through. If Abed was filming this he would literally be right in front of the gang, completely obscuring their view through it.
Deliberate mistake: In this episode, it is revealed Donna and Robert got together because Robert saved her from a water fountain. In "Another Bad Thanksgiving", it was shown Donna's sister introduced Robert to Donna. (00:02:20)