Bart and Barney sing "We're in the Money" on the way to the dog track
The scene with Bart's visit to Santa at the mall is homaged from the film (a disrespectful boy questions the identity of Santa)
Bart refers to A Charlie Brown Christmas
Bart sings the "Batman Smells" alternative to "Jingle Bells"
Bart refers to The Smurfs Christmas Special
Hewy discusses Christmas specials.
Rich mentions it. Also, poster is shown ("The Simpsons Christmas Special").
mentioned among traditional Christmas specials
Bart tells how the family acquired their dog for Christmas.
To remove his tattoo, Bart is strapped to a table with a laser moving towards him similar to Bond in this movie