Laws of Robotics & Party Rights - S6-E5
Continuity mistake: Jeff is facing Willy as Willy asks him where he was born. Still facing him, he responds, but before he finishes his sentence, the camera cuts and he is how facing completely away from Willy and is drawing on the chalkboard. (00:13:20)
Laws of Robotics & Party Rights - S6-E5
Continuity mistake: Jeff writes the word "Law" on the board and draws out his "born into dirt" story. A few cuts later, after Garrett asks him when he stopped being funny, the word "Law" looks much different, and the other parts look redrawn. (00:13:30)
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