All of Hesher's "persona", according to Joseph Gordon-Levitt, is inspired by late bass player from Metallica, Cliff Burton. Not only that, but the movie features a significant amount of music from the "Burton" era, including the solo that Hesher plays in the garage (Anesthesia, from the Kill 'Em All album) and, of course, the Hesher lettering.
In the scene where Hesher criticizes T.J. for not taking walks with his grandmother, the man who he refers to that rapes old women was actually serial killer Albert DeSalvo, more commonly known as the "Boston Strangler."
In the pool scene, Hesher asks R2 to shut down all the trash compactors. This refers to R2-D2 from Star Wars. Director Spencer Susser also directed a TV special short, R2-D2: Beneath the Dome (2001), and, of course, Natalie Portman played Queen Amidala in three Star Wars movies.
Elephants make several appearances in the film. Rainn Wilson's character is watching a TV show about elephants and we hear them in the background, the car dealership has a large pink elephant on the roof and beside TJ's bed there is a figurine of another elephant.