Visible crew/equipment: During the dream sequence, when Gilligan starts a showdown with Mr. Howell and the Professor, someone's face appears in the window in the background for a second, and it's none of the castaways - someone in the filming crew most likely.
Visible crew/equipment: As the flame is blown out by Skipper's sneeze from behind a board held by Gilligan, you can just see a man from Skipper's left blowing it out.
Visible crew/equipment: As the Skipper makes an 'X' in the dirt, the shadow of the camera rig raising up is seen on the ground.
Visible crew/equipment: As Wrongway says "A couple more minutes, I could've been killed", the studio lighting is reflected on the left lens of his goggles.
Pass the Vegetables, Please - S3-E3
Visible crew/equipment: As Mary Ann discovers she's blowing bubbles as she talks, you can see part of the device just to the left of her neck, and the bubbles can be seen coming from beside her left cheek.
Gilligan's Personal Magnetism - S3-E21
Visible crew/equipment: Toward the end, the group is around the table, talking about Gilligan. Then they see a pear and a bunch of grapes float over to a plate at the head of the table. Skipper goes over and addresses the invisible Gilligan. If you look at the top of the hut, you can see the wires used to make the fruit float. Also, earlier in the hut with Ginger, when Gilligan bit the pear, you can see the wire holding the pear as it shakes after the bite.
Gilligan Meets Jungle Boy - S1-E20
Visible crew/equipment: When Gilligan is floating inside the balloon and then outside, the wires supporting him are visible. (00:19:00)
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.
Visible crew/equipment: When Gilligan puts the Skipper down, you can see the wires attached to the corners of the lounge seat.
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.
Little Island, Big Gun - S1-E18
Visible crew/equipment: Gilligan shoots a bag of money in a tree with an arrow. As the money falls to the ground you can see a fan in the lower left corner of the screen aimed up towards the tree.
Visible crew/equipment: As the camera looks at Skipper and Gilligan, after the tossing of the sail, the edge of the studio tank is visible for a few seconds in the background.
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.
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.