You've Been Disconnected - S2-E17
Plot hole: Gilligan foils the rescue attempt by saying that before the storm, he wrapped up the telephone wires real good with the professor's rubber glue so they won't get wet... But the scene before this, all castaways were testing the phone when a storm instantly hit them without warning. Gilligan wouldn't have wrapped up the wires since there was no storm til the last second (in which they all ran and abandoned the wires).
Revealing mistake: In the dream sequence, the boss, E.V.I.L., is bald. You can see the line of the skin wig he has on.
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.
St. Gilligan and the Dragon - S1-E21
Continuity mistake: As the women are packing up to move out, Mr. Howell says he and Lovey have been married for nineteen years. As the men are trying to get to sleep, he says they were married twenty-two years.
Other mistake: All of their sheets were the same type. The sheet that the "Ghost" supposedly took from them was more silken, not the regular knit.
Operation: Steam Heat - S2-E25
Revealing mistake: When Gilligan and Ginger are in the cave at the volcano, you can see that the steam in the two passageway openings behind them is being shot in from jet nozzles.
Lovey's Secret Admirer - S3-E19
Other mistake: At the end of the episode when Gilligan is using the lie detector he says "I love spinach." The lie detector said it was a lie. But in the episode "Pass the vegetables please" spinach is his favorite vegetable.
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 Hunter - S3-E18
Revealing mistake: As Gilligan sits in front of a large boulder, the disguised charge that simulates a bullet strike is easily seen.
Revealing mistake: As the Professor and Skipper get the test vehicle rocking faster, there are a few times that the metal poles built into the table legs to slide it is visible. Then as Gilligan slides on the table, the channels the poles slid along are visible, and it's obvious that the figure flying out into the men's arms is a dummy.
Continuity mistake: After the vampire's wife (Ginger) unfolds the couch bed, she laughs with her arms down and spread out by her sides, but the next shot shows her hands up by her face, clutching her gown.
Continuity mistake: After the shark bites off the rest of the paddle, leaving the handle, Gilligan hesitates a second, sees no paddle, and begins swatting at the shark. A moment later, in the closeup, he's paddling, hears the bite again, and pulls the handle up, showing the paddle is gone.
Other mistake: The Communal Hut is built in the clearing, and has a dirt floor. When Skipper and Gilligan check outside, it's floating in the lagoon. But that suggests it had a wooden floor.
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)
Topsy-Turvy - S3-E10
Other mistake: At the end, after Mary Ann puts the pie down, and Gilligan drinks the juice, he hits the table, flipping the pie into the skipper's face. First, the Skipper starts to wince when Gilligan hits the table, preparing for the gag. Second, the pie tin defies physics by staying exactly in place on the board after the pie leaves it, and after the board bounces once and settles down. Third, Gilligan dips his finger directly into the cream on the Skipper's face, rather than missing a few times.
Topsy-Turvy - S3-E10
Continuity mistake: As the Professor cautions Gilligan about hallucinations, the long table is visible through the door. When the camera is close to the Professor and Skipper, the table is gone.
Topsy-Turvy - S3-E10
Continuity mistake: When Gilligan looks at the papaya tree, the fruit is yellow. When he gets to the tree, the fruit is green.
Continuity mistake: When Balinkoff shows Gilligan the control computer, it is off, but Gilligan is under control. A moment later, it is on.
Hair Today, Gone Tomorrow - S3-E8
Revealing mistake: After Skipper goes bald, you can see the line of the skin wig on him.
Hair Today, Gone Tomorrow - S3-E8
Revealing mistake: When Gilligan is bald, you can plainly see the line of the skin wig, as well as able to see his hair under it.
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.