When the Skipper is "locked" in the stocks, it's obvious the upper piece of wood is not locked at all. It moves up and down enough to reveal they are only pretending it's locked.
When the castaways are coming back to the island at the end, you can see some of the Los Angeles buildings in the background in the high camera angle.
When Gilligan is talking to the dog, trying to convince him that a dog goes "bow-wow", the sound of his bark can clearly be heard over the cat sound effect added to simulate the effects of the mad doctor's mind transfer experiments.
When Dr. Balinkoff's skiff sinks, the stem protrudes from the water revealing how shallow the lagoon set actually was.
It is never explained how Igor & Ginger's personalities get transferred to each other. It is clear that Balinkoff didn't do it because he is shocked when he enters the lab after the castaways have gotten free from the dungeon & discovers that Ginger's personality has been switched, as Igor arrives in Ginger's body. Igor couldn't have done it himself as it takes someone outside the booths, working the controls. Unless he could have put Ginger inside & locked her in a booth & then flipped the switch & hurriedly entered the other booth before the transfer was complete. Viewers also don't know what Igor's motivation for wanting to switch bodies with Ginger would be, other than curiosity and the viewer is never told. (Note: apparently, off-screen the castaways did it themselves, to have Igor (or at least his body) on their side, knowing they could be switched back later).
When Igor and the Mad Doctor are locked in the booths with the dog and cat, they somehow escape seconds later and are all shown running thru the castle.
The torture device the Skipper calls a stock is actually a pillory.