M*A*S*H - Never-nude Radar
In the episode "Sniper" in the second season, when Blake and Radar escape from the showers and rejoin the others, as Radar dashes through the door and sits down his towel flaps up briefly and his underpants are visible.
It was shown in a previous scene (when Radar tried to go and get help, but was forced back and lost his towel in the process) that Radar was not wearing underpants under the towel, and there's no way he could have got hold of any in between while trapped in the showers. He shouldn't be wearing any now!
(Presumably this is for the actor's decency, but it is still a slip-up as far as the character and plot are concerned.)