Other mistake: When Gilligan wakes up and tells everybody his dream, he hums the theme song from the movie Jaws. Nobody left the island yet so there's no way he'd know about the movie or even the music to it.
Rescue from Gilligan's Island (1978)
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Directed by: Leslie H. Martinson
Starring: Alan Hale Jr., Jim Backus, Bob Denver, Natalie Schafer
Genres: Comedy
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More mistakes in Rescue from Gilligan's Island
Mary Ann: He didn't mean any harm, Skipper.
Skipper: Neither did the iceberg that sunk the Titanic.
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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.