Aerodynamics of Gender - S2-E7
Visible crew/equipment: When Pierce's drone is following Jeff and Troy, as the two go through the bushes, you can see the string the drone is attached to as it "hovers."
Biology 101 - S3-E1
Visible crew/equipment: At the beginning of the episode, after Pierce rejoins the group and Jeff and the others begin to leave the room, watch Britta as she stands up. When she turns away from the camera, you can see the actress' microphone-pack in the back of her jeans briefly. (It's hard to spot but it's there, and is confirmed in the commentary track.).
Intermediate Documentary Filmmaking - S2-E16
Visible crew/equipment: When Jeff runs to the car which his father drives and opens the door of the driver, you can see the camera in the side window of the car. You can see it's a set camera and not a 'handheld type', the one that Abed is using during this episode.
Basic Crisis Room Decorum - S6-E3
Visible crew/equipment: While Chang is reading the message about the attack ad, you can see a very visible camera used to film Winger.
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