Advanced Introduction to Finality - S4-E13
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)
Contemporary American Poultry - S1-E21
Continuity mistake: An adhesive sign reading "Respect the Noble Animal" and a "Danger" sign behind Jeff disappear after the next reverse-shot. (00:11:54)
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.
A Fistful of Paintballs - S2-E23
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.
Cooperative Calligraphy - S2-E8
Character mistake: Right before Jeff searches Abed's bag, Britta explains to the group that Abed is the innocent one. After Jeff reminds her that Abed put gum in her hair, she looks at no-one in particular and says "empty the bag, Abed." Jeff is the only one holding the bag, with Abed standing five feet away from both of them. It's clear this line was directed to Jeff, but the wrong name was used.
Continuity mistake: The study-room on the second floor of the library, right next to a set of stairs, and the area isn't particularly bright. In the rest of the series, the study room (which is meant to be the same study-room) is now located on the first floor of the library, nowhere near any visible stairs and the area is much brighter and more well-lit. As often happens, the pilot was filmed before any other episode, and the setting was changed in the meantime.
Continuity mistake: In the very first shot, we can see there's a man with a dark coat, sunglasses, short hair and earbuds standing directly in front of the dean. When it cuts to the opposite angle, he's no longer there. When it cuts back to the first angle a few shots later, he's suddenly back.
Asian Population Studies - S2-E12
Continuity mistake: Right after the intro, the group is sitting in the Anthropology class waiting for Prof. Duncan. The chalkboard is filed with writing on it. When Duncan enters, the chalkboard is, except for the 3 top-corner titles, completely clean. (00:03:02)
Grifting 101 - S6-E9
Continuity mistake: When the grifting professor and Jeff are speaking in their office after meeting each other, we see the bottle of alcohol change amounts as the camera moves angles (from Jeff's POV to the teacher's). It is lower when the teacher is all alone, and there's more when it's Jeff's POV. (00:20:14 - 00:20:36)
Audio problem: We hear Troy say "you thought" while he is talking to Annie, but his mouth doesn't move. (00:01:15)
Basic Crisis Room Decorum - S6-E3
Visible crew/equipment: While Chang is reading the message about the attack ad, you can see a very visible camera used to film Winger.
Audio problem: A chef is being shot repeatedly by paintballs and heard screaming as he falls. However, his mouth never fully opens for him to scream as intensely as he was. (00:17:30)
Continuity mistake: Britta has a cellphone in her right hand. The camera cuts to behind her and she's flailing her right hand with no phone in it. In the next shot, the phone has jumped to her left hand. (00:13:05)
Laws of Robotics & Party Rights - S6-E5
Continuity mistake: Jeff writes the word "Law" on the board and draws out his "born into dirt" story. A few cuts later, after Garrett asks him when he stopped being funny, the word "Law" looks much different, and the other parts look redrawn. (00:13:30)
Laws of Robotics & Party Rights - S6-E5
Continuity mistake: Jeff is facing Willy as Willy asks him where he was born. Still facing him, he responds, but before he finishes his sentence, the camera cuts and he is how facing completely away from Willy and is drawing on the chalkboard. (00:13:20)
Queer Studies & Advanced Waxing - S6-E4
Audio problem: Elroy walks into the study room complaining about Donkey Kong stealing his idea. We hear him say they made "the eggs into barrels" but his mouth makes completely different movements. (00:00:55)
Lawnmower Maintenance & Postnatal Care - S6-E2
Continuity mistake: Elroy is holding the Dean in virtual reality. In real life, his hand is in front of his face and slightly opened. When the camera cuts closer, his hand is lower and clenched in a tight fist. (00:21:00)
Lawnmower Maintenance & Postnatal Care - S6-E2
Continuity mistake: Britta is running out of her parents' house, leaving the door behind her closing. In the next shot, the door has stopped moving and is opened up more. (00:16:55)
Lawnmower Maintenance & Postnatal Care - S6-E2
Other mistake: Britta hits Abed in the face with a pillow, swinging in from the right, but when it connects, his face swings the other way, the same direction from which the pillow came. (00:16:50)
Answer: The implication is that Jeff will still be teaching at Greendale after Annie and Abed leave. As for who became vice dean? It's never shown, since it's not really important to the series.
TedStixon