Advanced Documentary Filmmaking - S4-E6
Continuity mistake: Abed is making a documentary, and we see the fact that there are two cameras throughout the episode, so they are definitely acknowledged. However, in the scene at the trout fisherman's house, there is someone filming behind Annie and Troy and towards Annie and Troy. The problem being that whenever it shows Annie and Troy in front, there is no cameraman behind them, but when it cuts to behind them again there is somebody there filming.
Advanced Documentary Filmmaking - S4-E6
Continuity mistake: When the group is making posters for the MacGuffin Institute meeting, Annie holds up a poster saying "Welcome Archie" to show off name brand glitter but the character of Archie isn't introduced until the next episode (in which the banner shows up again). (00:03:11)
Suggested correction: This isn't a mistake. The episodes were simply aired out of order than the order they were produced. "Economics of Marine Biology" (production code 406), the following episode, was filmed before "Advanced Documentary Filmmaking" (production code 408).