The Psychology of Letting Go - S2-E3
Continuity mistake: When Professor Duncan comes into the classroom, he circles and underlines "anthropology." When Chang walks in, the circle and underline change drastically. It goes back to the original way in various shots.
Mixology Certification - S2-E10
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.
The Psychology of Letting Go - S2-E3
Continuity mistake: The amount of the black oil stuff that covers Annie when it spills on her increases in the next shot of her, before she and Britta start fighting.
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)
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