The part about the dog's kibble getting frozen to the porch and thawed with warm water and a spatula is from comic Tom McGillen's act. McGillen is a friend of writer Fred Wolf and also has a small part in the film.
The scene in which Joe, while working at the quarter toss booth at the carnival, sprays the plates down with PAM is a reference to his 1998 stand-up special Take The Hit in which he joked about trying to make a quarter land on a plate sprayed with PAM at a carnival.
The hardtop that Joe Dirt drove throughout most of the movie is a replica of a 1969 Dodge Daytona, a limited production car built for only one year during the muscle car era of the late sixties and early seventies. Only 503 of the real Daytonas were ever built.
According to Dennis Miller (on his radio show 11/26/2008) he has yet to see the movie, saying that "Someone told [him] there is a scene where fecal matter falls from an airplane and hits someone on the head," and this may not be his type of movie to watch. But likes that it gives him "caché with his kids' friends."