Biology 101 - S3-E1
Trivia: Not really a mistake, but something amusing to watch for. During the big opening musical number, watch Britta's face closely when Chang runs in. Right as he runs by her, her eyes squint in pain for a very brief instant and she reflexively mouths the word "Ow!" It's hard to see what's going on because it goes by quick, but it looks like the actor portraying Chang either accidentally kicked her in the shin or stepped on her foot as he ran in, and she reacted.
Biology 101 - S3-E1
Trivia: This episode aired Sept 22, 2011 where Abed learns season 3 of the (real life) TV show "Cougar Town" is moving to mid-season, which he fears means an upcoming cancellation. Abed and Troy say "6 seasons and a movie" in regards to the show (a line previously used in reference to "The Cape", another favourite show of his). While no movie was made, "Cougar Town" did move to mid-season in 2012 and lasted for 6 seasons.
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