The Science of Illusion - S1-E20
Visible crew/equipment: After Britta accidentally bumps the gurney into the window, she grabs the body bag in a failed attempt to keep the corpse from falling out into the quad. Right as she grabs the body bag, look on the ground behind her. Someone slides a mat in behind her for her to fall onto. (00:13:50)
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