Visible crew/equipment: As Gilligan runs along, stuck in the hollow log, the wires holding it up and guiding it are visible toward the top of the shot.
Revealing mistake: After the Skipper throws the attache case in the lagoon, it explodes. Problem is that the lagoon water and the water with the explosion are in two different areas, and where the explosion is, there was no case floating. Just markers floating where the explosive is placed underwater.
Pass the Vegetables, Please - S3-E3
Revealing mistake: As the camera pulls back from the hut, the bubbles can be seen coming from around the edges of the shot.
Pass the Vegetables, Please - S3-E3
Revealing mistake: As the Professor reads his meter, the bubbles are shooting from beside his nose, rather than his mouth.
Pass the Vegetables, Please - S3-E3
Other mistake: The spot where the coconut Gilligan tosses goes through is rounded, the suddenly squared in the close up. The wall in general is differently colored than the rest of the hut.
Pass the Vegetables, Please - S3-E3
Revealing mistake: When Gilligan picks up a coconut, the first one he crushes easily is totally different than the ones in the pile it's on, showing it was a specially made prop.
Pass the Vegetables, Please - S3-E3
Audio problem: As Gilligan gets up to lift the stool he was sitting on, we hear the sound of wood scraping on the floor, but it's on sand.
The Return of Wrongway Feldman - S1-E25
Other mistake: As the plane taxis in, there are tracks from the wheels in the sand prior to the plane's entry into the scene, showing a previous take.
Revealing mistake: After the Skipper tosses the sail into the water, look at the background. On the right side of the shot, the bottom of the backdrop is easily seen, showing this scene is filmed in a huge water tank set.
Revealing mistake: When the shark is attacking Gilligan's oar the second time, it stops completely for a couple of seconds.
Revealing mistake: As the shark goes by the floating bottle and towards the camera, the underwater rail the prop shark rides on is obvious.
Plot hole: Mr. Howell suggests the switching vodka for water idea, and then Gilligan empties one vodka bottle and puts water in it for the castaways. But there's no way this plan could have gone through since no castaway knew in advance how much vodka or how many bottles the Russians had to execute such a plan.
Revealing mistake: While they are at the front or side of the damaged boat, you can see that the dark windows above them are obviously painted on, rather poorly in some spots, and not real windows.
Topsy-Turvy - S3-E10
Factual error: When looking at the machetes the headhunters had, you can see the molded plastic handles on them. The natives wouldn't have access to such things.
The Second Ginger Grant - S3-E24
Revealing mistake: When "Ginger" (Mary Ann) forgets the words to the song, she asks the maestro, Mr. Howell, to restart the record. Before and after he puts the needle on the beginning, you hear the music, but the turntable isn't moving.
Plot hole: How could it be that every time someone or something was visiting the island during many episodes, they always made it back to civilization by the ending scene (as heard on the radio)? I can understand an actual person, but once anything else (such as a lion, a movie reel on a raft, etc.) leaves the island, it arrives perfectly by just simply slowly floating on the water with no human to guide them. Maybe the one exception could be the robot (programmed by the Professor).
The Friendly Physician - S2-E29
Other mistake: The whole time the control for the booths is operated, the handles are pulled towards the camera. In the final lab scene, Gilligan flips the lever towards the camera, but you can see the indicator reads 'OFF'.
Other mistake: When Gilligan and the ape are staring at each other, with the idea that the ape will stay hypnotized and ignore everything else, look closely at the ape's eyes. The actor in the suit glances twice and the Skipper and Professor as they pass.
Other mistake: As the Skipper is on the ground under the tree waiting for Ginger to get Gilligan, the headhunter is crawling behind him. You can see some smoke in the lower left corner, likely cigarette smoke from a crew member.
Answer: Bob Denver answered this when he was on a talk show hosted by Pat Sajak. He said they were going to write into an episode where the castaways found all these clothes, but it got too complicated, so he said, they decided, "who cares, it's only a TV show," and forgot about it. So the writers and actors even asked this, they just never bothered to address it.