Revealing mistake: When Gilligan is being pulled around in the water after getting on the hut boat, you can see the superstructure of the walls around the lagoon.
Revealing mistake: It's quite obvious that the lighting inside the hut they are tying the other huts to, is studio lighting, as candles or torches would have burned out from the storm winds.
Suggested correction: The castaways had a radio which always gave them information on the outside world (since being shipwrecked). Although usually the Professor used it the most, Gilligan has been seen in the original series listening to it himself, so he could have heard about the movie (out 3 years before the rescue) while still on the island.
Except that the Professor said that the radio hasn't worked in over ten years so Gilligan humming the theme song to Jaws would be impossible and all other current events wouldn't be known to the others either as they are asking about Jimmy Carter, Gerald Ford and Ginger asking about Watergate thinking it's the last name of a person.