The Friendly Physician - S2-E29
Plot hole: The scientist yells for Igor to capture the escaping Castaways, to which Igor responds "capture them yourself" in Ginger's voice. The scientist appears surprised to find out Igor is not Igor, but how can this be? He had to be the one to pull the lever to switch everyone's personalities and bodies around, so he should have already known.
Factual error: Sgt. Carter is wearing a plain belt buckle with his dress blues uniform. Since Sgt. Carter is Gunnery Sgt, he is a staff NCO so his buckle should have the USMC emblem on the buckle. (00:24:00)
Visible crew/equipment: In the first scene of the episode, a crew member is visible through an open door beside the staircase.
Double, Double, Toil and Trouble - S4-E4
Revealing mistake: As Serena gets hit by the pie her real blonde hair shows underneath, also, she wears minimal make-up for the only time.
The Addams Family Goes to School - S1-E1
Continuity mistake: After Mr. Hilliard goes through gate and nears the house, it's really at the real house. A second later, he's approaching the now-familiar front porch on the studio set. This is easy to tell because the layout of the two porches are radically different.