Flipper and the Bounty - S2-E13
Visible crew/equipment: After Bud wakes up all alone in Bligh's cabin, he soon realises all the doors are locked. Then, just as Bud rushes over to the stern window (particularly the second time), a seated crew member is visible at the bottom right corner of the screen; we can see the movement of a leg and two hands (so, it's not a mannequin).
The Alexander the Greater Affair (1) - S2-E1
Character mistake: When Alexander organizes the human chess game in his courtyard, the "pieces" stand the wrong way on the board, with a dark square in the lower right hand corner. That corner is always a light square. (00:22:50)
Continuity mistake: Aunt Clara crashes into the pagoda and is helped up by Darrin and Samantha. They head inside and you can see Aunt Clara's purse sitting in the pagoda to the bottom left. But when all three enter the house, Aunt Clara is now carrying her purse. (01:14:00 - 01:20:00)
Continuity mistake: When the door of Pod 1 opens after Jeff realises there is a saboteur on board, we see three vehicles in the pod and beside the Monobrake there is a red unit which has a windshield on it. However, when we see Chip appearing in the next shot, the windshield has gone.
Gomer and the Queen of Burlesque - S4-E21
Continuity mistake: On the company road on the base, the background changes from day to day. First there are white houses and trees, then the next day there are no houses, just trees and telephone poles. (00:09:00 - 00:19:00)
Other mistake: One of the natives putting the captured Seaview personnel into the cave is wearing laced up sneakers. (00:36:25)
Factual error: In the initial opening credits, there's a statement that the flying battle scenes were flown by the Air Force. At the time of the events depicted there was only the Army Air Corps. 1947 was the beginning of the Air Force.