Continuity mistake: In episode 11 of Season 4, it was stated that Leonard got an A in 1968, then opted for pass/fail to have the highest GPA in the college. In the final scene of this episode, however, it shows Greendale college as being established in 1974.
Continuity mistake: You can see the play director telling a pianist with grey hair to "play something modern." About twenty seconds later when Britta throws her tea hat off towards the pianist, however, it's an entirely different piano player now, that has brown/black hair. (00:17:10)
Other mistake: During Leonard's "Let's Potato Chips" YouTube video during the ending credits, you can see the video reaches the end of the load/play bar (watch the circle), yet the video continues for several seconds. Once the circle reaches the end of the load/play bar, the video is over and won't continue.
Continuity mistake: Near the end, when Jeff says to Troy "you're a man now" the camera goes onto Troy and we can see Abed asleep on Britta's shoulder (Britta is also asleep), even though in the shot before that, they were both awake. Then after the shot of Troy we see Britta and Abed awake again.
Character mistake: Annie when giving her gifts is holding two little mini flags to cover the possible ethnicity of Shirley's baby. One is a Chinese flag and the other is Zimbabwe. Annie makes reference to the fact that the ethnic food she made is one from Ghana. She makes Ghana ethnic food but does not get the right flag for Ghana. She decorates the table with numerous flags which are also Zimbabwe.
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.
Revealing mistake: When Chang is getting blasted with the minigun, the safety pads under his shirt are very noticeable. (His shirt is extremely "puffed out" and you can see the outline of pads.) He's been tied up most of the episode and wasn't wearing pads earlier, so there's no way he was able to get pads on in the meantime.
Continuity mistake: When Annie starts to throw her tantrum, she knocks stuff off the table, including the microphone and small mic stand. When she's lying on the table, the mic stand is back on the table. It back on the floor when she and Jeff leave, although the Uruguay sign is now back on the table.
Continuity mistake: When Britta is in a cage, before Chang walks in, a couple pass her and are walking out the double doors, where both doors are open. After Chang steps up to the cage and the camera shot changes, the couple is further away from the doors and walking out again, only this time one of the doors is closed.
Character mistake: At the party, Jeff is talking to Ted about his parents' divorce, which included a custody hearing. Jeff mentions the divorce lawyer drove a Mercedes SLK. However, the SLK didn't come out until 1996, which would make Jeff at least 21 (turning 22) at the time of the divorce (he was born Nov 1974). There would have been no need for a custody hearing (Jeff was an only child between his mom and dad) and his parents divorced when he was very young, so the divorce had to happen prior to 1996.