Can we take a lesson from this. The dictionary says that EXPOSITION is a setting forth of meaning or intent.
As writers we all need to present the most information possible in a timely manner without scaring away the reader. You want them to identify with the characters and the story from page one. By naming the characters the skipper, the millionaire, his wife, the movie star, the professor... etc. He gave a very clear idea of who it was and what their immediate difference were. All from very different walk of life. How do you describe you hero and heroine? Are you able to give a clear, immediate image of them that will intrigue the reader and make them want more? If not, maybe you need to look at it again.
In the meantime, ponder these...
Why did Ginger bring so many clothes on a three hour tour?
If it was a deserted island and they couldn't get off of it, how come there were so many guests who could get on it and then disappear once again?
Just how did they get that radio to work off coconuts?
A bit of trivia...
Incidentally, in the opening scene you can see a flag at half mast. This was filmed in the wake of the assassination of JFK. Also, the original theme song was called "The Ballad of Gilligan's Isle" not Island.
While we will never actually know what Gilligan's full name was, I did discover that the Skipper's name was actually Jonas Grumby, played by Alan Hale.
And finally... The theme song has been covered by Bowling for Soup (here) among many others. There were several other version before they picked the one most of us (of a certain age) remember and can sing by heart. One was an unaired Calypso version for the Pilot written by John Williams (here).
So, for now... just sing along with me. You know you remember the words.