When the Doctor and Professor contradict the Skipper's scolding of Gilligan's suggestion for the two sailors to sail the boat to the Doctor's island first, the Skipper says, "Well, nobody likes a showoff!" At the end, when Gilligan is criticizing the Skipper's assessment of the just sunken boat, the writing appears to have the Skipper give a call back to this earlier comment. However, it doesn't match up as this time the Skipper says, "Like I said, nobody likes a wise guy!"
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 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 Dr. Balinkoff's skiff sinks, the stem protrudes from the water revealing how shallow the lagoon set actually was.
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.
Has a sailor, Gilligan would know how to tie certain knots. The fact that he was tying off the rope to the boat on a tree branch was not believable for someone that was supposed to have a lot of experience as a sailor.
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 boat The physician traveled on to the island was taken back and forth numerous times yet when The castaways came back together their things the boat sank have to bringing all seven of them back to the island. Not believable.
The torture device the Skipper calls a stock is actually a pillory.