The title is a reference to the Broadway musical "The Unsinkable Molly Brown" (1960). The musical depicted the life of the socialite Margaret Brown (1867-1932), a famous survivor of the sinking of the Titanic.
The van that delivers the kitten has a greyhound logo, similar to the one used by the bus company.
Chuck Jones, who would animate Comment le Grinch a volé Noël ! (1966), was already using some of the facial characteristics which would be seen on residents of Whoville in the future production. Tom and the kitten are two notable examples.
The colorful background images have become more abstract and streamlined here, as befits the emerging design style of the space age 60's.