Pass the Vegetables, Please - S3-E3
Continuity mistake: The radiation meter the Professor reads disappears between shots.
Operation: Steam Heat - S2-E25
Revealing mistake: After Gilligan says his line about the earth swallowing them all up, an explosion rocks the area. Between the end of the line, and the rocking, there's a split second of blackness indicating a cut between the line and the action.
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.
Will the Real Mr. Howell Please Stand Up? - S2-E26
Revealing mistake: When Gilligan demonstrates his man-made wings, when the camera goes close up to him, you can see the wires.
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.
The Producer - S3-E4
Continuity mistake: Harold Hecuba (a.k.a. H.H.) goes out to change costumes. When he comes in as Ophelia the stage door first closes behind him, then falls off the hinges. The shot cuts to the Castaways, then back to H.H., and the door is back on the hinges.
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.
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.
Pass the Vegetables, Please - S3-E3
Revealing mistake: When Gilligan tosses the coconut, as it flies past the Skipper, the line it slid on catches the light as it shakes.
Other mistake: Ginger keeps hoping that the play will help her be discovered. But according to what we know, she's already a famous movie star.
Castaways Pictures Presents - S2-E7
Plot hole: During all their filming for their "silent" movie, the castaways are using talking in actual dialog to explain their overall situations on the island, but when played back at the end, it's just showing them all talking sped up without hearing voices being a silent picture. What was the point of them filming then with actual words? They may as well just moved their mouths randomly without actual words coming out. In addition, where did the "music" come from throughout the movie?
Pass the Vegetables, Please - S3-E3
Revealing mistake: After the Professor puts everyone to sleep reading the book, the camera backs up, showing the straight seams of the soundstage floor where the set ends.
Pass the Vegetables, Please - S3-E3
Continuity mistake: The book the Professor is reading to the others immediately switches from being lower to higher as the scene cuts.
Pass the Vegetables, Please - S3-E3
Revealing mistake: The guide wire used to "throw" the coconut through the hut by Gilligan is visible.
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.
Good Night Sweet Skipper - S1-E5
Continuity mistake: When the Professor drops a couple of tranquilizer pills in the Skipper's cup, it's nearly filled to the rim. As he hides the bottle of pills, the liquid is a little lower.
Voodoo Something to Me - S1-E4
Continuity mistake: As the Professor comes up to Skipper and the girls, his left hand goes up to his face, but a second later it's his right hand on the bridge of his nose.
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.
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.