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.
Morticia and the Psychiatrist - S1-E2
Continuity mistake: When Morticia is watching Gomez and the trains, at the second of the collision and explosion, it's a re-use of the shot when Mr. Hilliard is there, as in just a split second, you can see him, then there's Morticia again.