Continuity mistake: As Gilligan marches over the cliff, he's wearing Skipper's hat. As he's hanging on the branch, his regular white hat is on his head.
Continuity mistake: The professor mentions he can't drink vodka with the Russians because he's allergic to alcohol, yet in the episode "Man with a Net" (with Lord Beesley), he drinks a strong alchoholic drink he made along with everyone else with no signs of any sickness, or reaction preventing him from drinking it.
Operation: Steam Heat - S2-E25
Continuity mistake: When Howell is talking to Gilligan, the ground apparently trembles due to a volcano. Before the rumble, Howell's Safari hat brim is bent up on the left side. After the cut to the Professor, the right side is bent upward.
Continuity mistake: When Gilligan falls off of the cliff at the end, he is wearing different clothes and facing a different way than he was when he fell off.
Beauty Is as Beauty Does - S2-E2
Continuity mistake: We see a shot of the outside of Ginger's hut when she and the Skipper are first planning for the beauty contest. The door to the hut has a window in it and we can see the Skipper's hand leaning on the sill. We cut inside and suddenly Ginger is by the door and the window has vanished.
The Friendly Physician - S2-E29
Continuity mistake: The color of Ginger's shoes are different once returning to the island at the end of the episode from what she wore on the mad scientist's island.
Operation: Steam Heat - S2-E25
Continuity mistake: The professor wound the clock on the bomb by turning the hand to nine. A second after it was tossed in, it reads eight. It then takes about about fifteen seconds between the numbers to get to zero.
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.
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.
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.
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.
Don't Bug the Mosquitoes - S2-E12
Continuity mistake: As Gilligan plays the drums, he shakes his head wildly, and the shades fly off. A moment later as they finish their song, Gilligan knocks over a drum, and it's up in the next shot.
Castaways Pictures Presents - S2-E7
Continuity mistake: At the end of the filming, the Professor is drawing a line down the east coast of the United States on the board. When watching the film, the line is missing at the end.
Castaways Pictures Presents - S2-E7
Continuity mistake: After Mary Ann drops the basket, two pieces of fruit pop out of it. When Gilligan goes to pick it up, he picks up several pieces.
Castaways Pictures Presents - S2-E7
Continuity mistake: As Thurston calls cut, in the wide shot Gilligan stops and his spear dips with the tip down. In the closeup, Gilligan is now holding the spear straight up by his side.
Castaways Pictures Presents - S2-E7
Continuity mistake: The amount of rope around Mary Ann varies between shots.
Beauty Is as Beauty Does - S2-E2
Continuity mistake: They used a standard electric phonograph. Later on, the phonograph is a bamboo and wood device with a ship's wheel as the turntable. It had to be cranked like the old Victrolas to work.
Continuity mistake: When Skipper tries on the sheet to teach Gilligan not to be scared, we see him putting it on and it is solid white. However, when Gilligan says he isn't scared he says it is because a "ghost doesn't wear a sheet that says S.S. Minnow on it." Now the sheet has wording on it. (00:08:45)
Continuity mistake: As Rodriguez goes back to Ginger, the Skipper straightens his hat. In the closer shot, Skipper straightens his hat again. (00:09:55)
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.