The Year Santa Got Lost, which Homer briefly sees on TV, is a parody of the Rankin/Bass stop-motion Christmas specials. The character of Mr. Mailman is based on S. D. Kluger from Santa Claus is Comin' to Town, and several of the Misfit Toys from Rudolph the Red-Nosed Reindeer make cameo appearances.
During the decoration montage, Marge hangs mistletoe and is soon kissed by Grandpa and Homer sets up a plastic deer on the front lawn, which is shot by Cletus and his redneck friends who plan to eat it.
During Krusty's holiday special, Krusty remarks Kent is getting last years' holiday meal pumped out his stomach.
In addition to giving Homer a DVD player, Carl also gives Homer the first season of Magnum, P.I., even though this episode aired in 2003 and the first season of Magnum, P.I. did not come out on DVD until 2004. However, it is still 2003 because Lisa mentioned it was Saturday, December 6 and December 6 was on an Saturday that year. Lisa also mentions that A Christmas Carol was written 160 years ago. That is 1843, which is exactly 160 years before 2003.