In several scenes where H.I. is in the factory where he works his work suit has a "Hudsucker Industries" patch on it. The Cohen brothers who directed and produced the movie also put out a movie a few years back called "The Hudsucker Proxy."
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When the biker is riding into town in HI's dream and throws a grenade at a rabbit, it resembles the scene in Monty Python and the Holy Grail where they throw the Holy Hand Grenade at the killer rabbit.
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When H.I. is robbing the convenience store while Ed and the baby wait in the car, listen to the music coming over the store's PA. It's a cheesy muzak version of the banjo music used throughout the film.