Little Island, Big Gun - S1-E18
Visible crew/equipment: At the beginning of the episode when Ginger comes out of the hut the shadow of the boom mic is visible on the hut.
Visible crew/equipment: Outside the Howell's hut as the castaways ready to leave the island, the shadow of a boom mike enters the upper left side of the scene twice.
Other mistake: On the beginning, the butterfly Beasley calls the Pussycat Swallowtail is yellow. Later it's orange. Also, when Beasley holds the cage with the painted butterfly, you can see the wires making the puppet move.
Visible crew/equipment: When Gilligan puts the Skipper down, you can see the wires attached to the corners of the lounge seat.
The Friendly Physician - S2-E29
Continuity mistake: After Skipper admonishes Gilligan for his suggestion, Balinkoff says "No, no", and starts to gesture with his right hand. After the angle change, he starts to gesture again.
Pass the Vegetables, Please - S3-E3
Other mistake: The book the professor is supposedly reading radiation information from has an odd decoration on the cover over the title. It is actually technical manual TM 9-729 for the M24 Chaffee Light Tank.
Pass the Vegetables, Please - S3-E3
Continuity mistake: When the camera is in wide shot of the table scene where everybody fainted at the Professor's announcement, he has the book at belt level. In the close up, he has it at chest height.
Continuity mistake: In the hut, "Gilligan" has the spoon of his transmitter knife open so his commander can hear the conversation. In the wide angle shots, the spoon is half way out. In the close ups, it's fully in position.
Ship Ahoax - S2-E23
Continuity mistake: The Professor is under the table which has a cloth positioned so he can't be seen. However, in the shots of him, you can see the background, and nobody's feet or the cloth.
Visible crew/equipment: When Gilligan is packing, Skipper sneezes and blows out the candle. The third time, Gilligan blocks the candle, and if you watch the right side of the screen, you see the tip of somebody's nose pop into the scene as he blows out the candle.
Revealing mistake: When Skipper is blindfolded, as he rears back getting ready to sneeze, watch his right shoulder. You can see the line that pulls the blind off when he sneezes.
Continuity mistake: In the opening credits, the boat used as the Minnow changes. It goes from having an upper steering deck, to flat topped and different colored, and back.
Revealing mistake: When Skipper is sneezing after Gilligan showered, he turns towards the wardrobe. As he sneezes, in a "blink and you miss it" moment, the line pulling up the bottom of the green cloth is momentarily visible, pulling from the upper right corner of the screen.
Operation: Steam Heat - S2-E25
Continuity mistake: As Thurston tosses a packet of money away, his arm goes full circle, before his hand rests by his mid section. When the camera cuts, his right hand is over the edge at his wrist.
Other mistake: Mary Ann comes up to the Skipper while he's learning to juggle. If you look closely, the coconut bounces on the ground a couple of inches from his left foot. When Gilligan approaches, the coconut bounces off the bottom shelf. And in both times, the Skipper reacted in pain.
Ship Ahoax - S2-E23
Continuity mistake: When Ginger holds up the Three of Clubs, her fingers are covering the bottom Club on the card. When the shot cuts to her in close up, her fingers are behind the card, with her thumb partially covering the bottom 3.
Gilligan's Living Doll - S2-E21
Other mistake: When the Howells give their suggestions, if you look at the dark rectangle, you can see the word REJECT before it lights up. Likewise, when Ginger talks to it, you see TILT before it lights up.
Revealing mistake: When the Professor comes over to the Robot to ask "How would you like to do us a favor?", look closely at the mesh like part of the Robot's "face", just left of the vertical black bar. You can see the Robot actor's eye blinking and looking around. When he nods, you can see the outline of the actor's head.
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.