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)
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)
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