During HH's 2nd attempt to perform "To Be Or Not To Be," the set door he enters in clearly falls off its hinges just before a quick cut to the captive audience. After the cut back, the door behind him is intact and closed.
This is the only Gilligan's Island episode that had two directors. Ida Lupino injured her foot on set in the middle of the shoot. George Cahan was brought in and finished the episode on schedule.
Theme of episode: As Shakespeare himself said, "Love all, trust a few."
The casting for the Hamlet musical is thus:
Mr. Howell: Claudius
Mrs. Howell: Gertrude
Mary Ann: Laertes
Professor: Narrator (?) and record player operator
Phil Silvers owned a stake in the production company responsible for the show.
Two of the songs in the play are words written from music straight out of the classic opera Carmen. "To Be or Not Be" is sung to the melody of the "Habernera" aria. The song sung by Polonius "Neither a Borrower nor a Lender Be" was sung to the melody of the "Toreodor" march. The third piece, "Hamlet, Do Be a Lamb" was reported to be set to the melody of Schubert's Baccarole. Who said there was no culture on Gilligan's Island?
Hecuba: The castaways try to impress producer Harold Hecuba by performing Hamlet. Hecuba was a mythological figure mentioned in Hamlet's second scene of Act II.
Gilligan (as Hamlet): "Hide any place... but, don't go near the water!"
After hearing the approach of her father and brother, Ophelia claims she must be not be found with Hamlet and must hide. She questions Hamlet where she should conceal herself. Hamlet's reply, in this condensed retelling, is to hide anywhere but not to go near the water. This is a clever in gag since Ophelia meets her demise in Hamlet by drowning.