Besides Butch Hartman's portrait, the "eight oddball wishes" that Cosmo and Wanda produce include a toilet, an old-time bicycle, a donkey carrying a suitcase, a giant set of false teeth, a big toy submarine (which looks like the one Wanda transforms into during the song in "Christmas Every Day!"), a bowl of cereal, and a plastic whale (which resembles Big Ben).
The music that plays when Winter Squidlock sings, the "six jamming jellies" line is a background music piece titled "Stadium Rave," originally used in the episode, "Jellyfish Jam."
When Vicky stops singer her part of the song, her legs twirl up. This is is a reference to when the Wicked Which of the East dies in Wizard of Oz.
The elf that looks like Jimmy being chased by the elf that looks like Carl's clones is a reference to the Jimmy Neutron interstitial short, "Carl Squared".
The elf that looks like Patrick on top of the pine tree at the end of the short is a reference to "Christmas Who?" when Patrick jumps up on top of the coral tree during the song, The Very First Christmas.