Dewey Cox's audition, at which he sings Dean Martin's hit "That's Amore," is an in-joke reference to Elvis Presley. Elvis showed up at his audition for Sun Records wanting to sing like Dean Martin, but Sun owner Sam Phillips refused to record him until he and three members of the Sun house band started jamming on a blues song, Arthur Crudup's "That's All Right, Mama," which became Elvis' first record.
When we see the Top Selling singles chart showing Deweys fictional hit song "Walk Hard" at #4 the 3 songs ahead of it are #1 You, You, You by The Ames Brothers, #2 No Other Love by Perry Como and #3 P.S. I Love You by The Hilltoppers - all of which were actual hits.
When L'Chaim visits Dewey in prison he begins talking in Yiddish asking Dewey to speak the "Mamehlushen" (literally meaning "mother tongue") explaining that the guards won't understand what they're saying and suggests Dewey go to rehab. Dewey responds in German.
After Darlene (Jenna Fisher) and Edith (Kristen Wiig) both walk out on Dewey in the hotel room, the way Dewey chases after them down the street is a parody of the T1000 running in Terminator 2: Judgement Day (1991).
The trivia item below may give away important plot points.
A few scenes in the movie involve a grown up Dewey Cox (John C. Reilly) having conversations with the spirit of his dead brother Nate (Chip Hormess), only to find that Nate, even though he died as a boy, has grown older (and is played as an adult by Jonah Hill). "Walk The Line", the Johnny Cash biopic that "Walk Hard: The Dewey Cox Story" is primarily parodying, detailed Johnny Cash's struggle to cope with his older brother Jack's accidental death, but never featured Johnny Cash communicating with his late brother's spirit. However, in "Cash: The Autobiography", the basis for "Walk The Line", Johnny Cash wrote about how he routinely spoke with Jack into his own adult years. Cash also noted that Jack's spirit got older as Johnny Cash himself aged, and always remained two years older than Johnny.