Jimmy being chased by Carl's clones is a reference to the Jimmy Neutron interstitial short "Carl Squared".
In spite of certain things happening to the characters during their respective lines, (such as Jimmy being chased away by Carl and his clones, and Vicky collapsing under the portrait), they still appear in their original positions in later shots.
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 Squidward sings the "six jamming jellies" line is a background music piece titled "Stadium Rave", originally used in the SpongeBob SquarePants episode Jellyfish Jam.
Patrick on top of the pine tree at the end of the skit is a reference to Christmas Who? when Patrick jumps up on top of the coral tree during the song.
Vicky's hair is colored brown, instead of red-orange, as it is on the show (The Fairly OddParents).