Marge's attack on Hitler in the movie theater parodies Quentin Tarantino's film 'Inglourious Basterds.'
During the puppet sequence, Grampa and Jasper appear in a theater box heckling the family. This is a reference to Statler and Waldorf, the two old men who typically do the same thing to the Muppets.
The abominable snowman (or Bumble) from "Rudolph the Red Nosed Reindeer" can be seen sweeping up in the background.
The title is from "'Twas the Night Before Christmas" or "A Visit from St. Nicholas" first published anonymously in the Troy, New York Sentinel on December 23, 1823 by Clement Clarke Moore. Further study, however, lends credence to the authorship of Henry Livingston as none of Moore's extant poetry displays any sense of good humor.
In the first segment, Santa has a figurine on his desk which resembles Sam, the snowman narrator of "Rudolph the Red Nosed Reindeer."