This is a rare occasion in The Simpsons in which the couch gag at the end of the title sequence (in this case the Simpsons falling on and destroying the couch) is actually incorporated into the episode's plot.
Rev. Elijah Hooper mentions the Fight Club (1999) near the end of the episode. Edward Norton, who voices him, starred in Fight Club alongside Brad Pitt.
The "Day by Day" song that plays during the montage scene contains the same lyrics as Greg's (Ben Stiller's) improvised prayer over dinner in Meet the Parents - one of the movies referenced by Reverend Elijah (Ed Norton).