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.
Don't Bug the Mosquitoes - S2-E12
Character mistake: When the "Honey Bees" (Mary Ann, Ginger, Mrs. Howell) perform, Mrs. Howell (Natalie Schafer) messes up her lip-syncing throughout the number. But it is most noticeable at the very end when the girls put their heads together and say "buzzzzzzzzzzz" but Mrs. Howell is mouthing an "oooooooooo" which she changes to a "zzzzz" mid-way through the note.
Revealing mistake: After Gilligan lies down on his hammock, there is an "X" in the sand where actor Alan Hale, Jr. stands. Obviously it is the mark where Hale is supposed to stand, and he does stand there as he speaks to Bob Denver.
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.
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.
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.
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.
Other mistake: When Mrs. Howell looks at the lion in the mirror, the image is not reversed as it should be when the camera looks directly at the lion.
Gilligan's Living Doll - S2-E21
Revealing mistake: Watch the window on the barrel used as a washer. It looks to be somebody inside wiping the glass to simulate clothes washing.
Other mistake: In the opening scene, and later, the camera shows the Howells' hut, but the scene is in Skipper and Gilligan's hut.
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.
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.