Other mistake: At the beginning of the episode when the Skipper wakes up on the boat this scene is actually from the original pilot, as you can see the 3 different actors that played the part of the professor, Ginger, and Mary Ann. (00:01:20)
Suggested correction: The original actors ARE shown, true. However their characters slightly differred in the original pilot. They were known as a high school teacher, Ginger, and Bunny.
Continuity mistake: While the castaways are standing around while their clothes dry, Mary Ann is not wearing any shoes. As the scene continues she is shown standing wearing black shoes. (00:05:00 - 00:06:00)
Continuity mistake: When the SS Minnow is shown beached on the deserted island, it's seen leaning on its left. At the ending credits, the Minnow is shown completely upright.
Plot hole: How could it be that every time someone or something was visiting the island during many episodes, they always made it back to civilization by the ending scene (as heard on the radio)? I can understand an actual person, but once anything else (such as a lion, a movie reel on a raft, etc.) leaves the island, it arrives perfectly by just simply slowly floating on the water with no human to guide them. Maybe the one exception could be the robot (programmed by the Professor).
The Friendly Physician - S2-E29
Other mistake: The whole time the control for the booths is operated, the handles are pulled towards the camera. In the final lab scene, Gilligan flips the lever towards the camera, but you can see the indicator reads 'OFF'.
Other mistake: When Gilligan and the ape are staring at each other, with the idea that the ape will stay hypnotized and ignore everything else, look closely at the ape's eyes. The actor in the suit glances twice and the Skipper and Professor as they pass.
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.