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.
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