Revealing mistake: When Dr. Cox is duct-taping Dan to the bathroom wall, you can see that the tape across Dan's forehead is already stuck before Cox sticks it.
Revealing mistake: When Dan is in the tub you can see his dark swimsuit in a few shots.
My Boss's Free Haircut - S4-E20
Revealing mistake: When Carla and Elliot are walking through the graveyard, Elliot falls into an open grave. After she has fallen off the bottom of the screen, you can see her ankle flick up in the bottom of the picture, showing that she actually just fell down on the floor during shooting.
Answer: Dan was drinking beer and Cox feared that Dan might get so intoxicated he would fall asleep and drown in the tub.
Mortug