Big Man on a Little Stick - S1-E22
Continuity mistake: As the Professor sends Duke off, he gives the island's position as 110° Latitude, 10° Longitude. In "X Marks the Spot" (S1: E: 19), the position is given as 140° Latitude, 10° Longitude.
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.
Other mistake: When the headhunter is about to chop a tree Gilligan is behind, he yells. The actor has metal fillings in his teeth. Headhunters would not likely have a dentist.
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.
Other mistake: As Mary Ann pedals to power the sewing machine, the bobbin only clicks back and forth, giving the illusion of real movement.
Revealing mistake: When Mr. Howell and the Professor are thrown by Gilligan and the Skipper, during the struggle you can see Gilligan flying in from the right side. But it can easily see that it is a dummy in Gilligan's clothes.
They're Off and Running - S1-E29
Other mistake: In several shots during the first turtle race, Gilligan is inexplicably wearing a wedding band (Bob Denver was married to his first wife at the time and forgot to remove it). (00:01:00 - 00:03:00)
Continuity mistake: At the end after Gilligan pretends to throw away the Eye of the Idol, everyone gets up to look for it. As the Professor gets up, Gilligan gestures to him. In the next second, his arms are on the table.
Chosen answer: It looks like a mistake to me I see it when the Professor is put into a trance, but it is not there later.
Bowling255 ★