Continuity mistake: When Jeff goes into Ian's office and sits down, he puts his book down so the spine is facing the viewer's right and puts his drink on top of it. Later, without touching the book, it is rotated 90°.
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.
Spanish 101 - S1-E2
Continuity mistake: When Pierce pours him and Jeff a glass of whiskey, two glasses are shown and he pours whiskey into only one of the glasses. In the next shot, both glasses have whiskey in them. (00:09:25)
Spanish 101 - S1-E2
Continuity mistake: When Jeff and Pierce are having a glass of whiskey, Pierce makes a toast and Jeff replies "To the irony of that sentence." After he says this, Jeff puts his glass back on the table and Pierce lowers his glass, but doesn't put it back on the table. In the next shot, Pierce's glass is suddenly on the table. (00:09:35)
Spanish 101 - S1-E2
Continuity mistake: When Pierce tells Jeff that Britta is ugly, Jeff takes a drink from his glass of whiskey and puts it back on the table. In the next shot, there is suddenly much more whiskey in his glass. (00:09:50)
Continuity mistake: After Abed shares his film, his dad leaves the room. Abed raises his arm and points to his dad. The camera cuts to a different view of Abed and he raises his arm again. (00:19:00)
Continuity mistake: During the scenes in the pool area and the locker room, posters can be seen in the background with the Greendale Human Being on them. However, the Human Being mascot isn't invented until the next episode.
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)
Romantic Expressionism - S1-E15
Continuity mistake: At the start of the dance, the Human Being and its partner can be seen dancing on the dance floor, but a few shots later they can be seen entering the room over Jeff's shoulder.
Continuity mistake: The "windmill" Pierce draws changes in between shots when the Changs arrive.
Continuity mistake: After the pottery class scene, in the Spanish classroom, when Britta and Jeff are talking, his right arm is across the desk. When Jeff replies "so did someone's psych teacher" and camera cuts, his arm is suddenly folded up by his chest. In the next shot, his left hand is suddenly over his right hand.
The Science of Illusion - S1-E20
Continuity mistake: When Shirley and Annie chase Jeff, they're wearing their seat belts. In one shot you see Annie doesn't have her seat belt on, but in the next shot it's back on.
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)
Contemporary American Poultry - S1-E21
Continuity mistake: When Jeff and Abed are talking in his room, the amount of the root beer float in Abed's glass changes. Especially noticeable is when Jeff leaves, the float goes from near the top and above his fingers to a couple fingers below.
Contemporary American Poultry - S1-E21
Continuity mistake: At the end when Abed is talking to the Dean, there's an open to-go box with chicken fingers. After the Dean asks who would steal a box of hairnets, it cuts back to Abed and the box and ketchup are gone. Post-it notes are also now seen and the stapler moved. In the next shot of Abed, the chicken is back.
Continuity mistake: When the 7 go outside, Troy is talking to Shirley, he takes his toothpick out to say he's not an ambassador, but in the next shot the toothpick is back in his mouth.
Continuity mistake: After Jeff and Britta have had sex, when Britta is pointing her gun at Jeff, in shots behind Jeff she is holding the gun sideways, but in shots from behind Britta she is holding it straight.
English as a Second Language - S1-E24
Continuity mistake: When the class leaves the Spanish classroom so Chang can talk to Jeff, in one shot Annie only leaves her audio recorder on her desk, but in the next shot her textbooks are suddenly there.
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