Visible crew/equipment: On the Constellation, the camera is looking at the man helping Kirk to get the secondary view screen working. As the camera goes to pull back to allow Kirk into the shot, you can see the shadows of the camera shades on the wall. (00:25:00)
Visible crew/equipment: When Vaal is not fed and he starts spewing smoke everywhere, you can see a volcano type firework going off just inside his mouth. (00:43:55)
Answer: Kirk was getting his physical and Dr. McCoy probably turned off communications, because if he hadn't, Kirk would have left and headed straight for the bridge, leaving McCoy irritated.