The song that Will and Judy are singing is "Sloop John B" and although it was recorded by The Beach Boys and included on their album "Pet Sounds" in 1966, it actually was a very old Bahamian folk song from Nassau. A transcription of it was first published in 1916 and a version of it was actually included in Carl Sandburg's The American Songbag in 1927.
Chavo hands Will a pointy red-yellow-green thing on a stick and says, "For good muchachos, I have candy." Astro Pops were lollipops developed in 1963 by two rocket scientists. The three flavor candy, supposedly representing a three stage NASA rocket, became very popular during the height of the Space Race.
During the duet between Will and Judy performing The Sloop John B, Bill Mumy is actually playing the guitar, as Bill has had a career in music, notably with Barnes & Barnes (Fish Heads).
The ice block containing the princess was originally a prop in the classic 1951 science fiction film, The Thing from Another World (1951)
Dr. Smith refers to the robot as John Barleycorn. This is a reference to the robot's earlier drunken state.