The Coon Chicken Inn was a real restaurant chain, founded in 1925 in Salt Lake City. However it folded in the late '50s and never changed its name to Cook Chicken, as in the film.
According to director Terry Zwigoff, Steve Buscemi was so uncomfortable playing the role of Seymour that whenever shooting was finished for the day, he would immediately change his clothes so he could look completely different.
When Enid and Rebecca are following the "Satanist" couple, we see them walking down a street with a storefront to their left and a crosswalk sign behind them. They turn a corner with the building on their right, but then we them walking down the street with the storefront once again on their left and crosswalk sign behind them.
When Enid rips open the wrapper of the champagne/sparkling wine there is no metal wire around the cork. There is always a metal wire (because of the pressure that is inside the bottle).
When Enid and Rebecca are at the diner and Enid is looking through the personal ads, reading them aloud, Rebecca is playing with sugar on the table. She forms shapes in them that change unnaturally every time the camera goes back to her