Jim Jarmusch said he wrote the role exclusively for Bill Murray, of whom he is a big fan. He planned another film to work with him, then changed his mind and then changed his mind again: Bill Murray is appearing in The Limits of Control (2009), Jim Jarmusch's next film.
Jim Jarmusch finished the script in two and a half weeks.
Sun Green is also the name of a young girl featured in the Neil Young album "Greendale". Jim Jarmusch is a big fan of Neil Young.
This project's working title was "Dead Flowers", a possible reference to a song on The Rolling Stones album "Sticky Fingers".
Bill Murray's son, Homer Murray has a quick role at the very end of the film. He looks into the camera as the car he is in passes by.
Jim Jarmusch asked each of the four female leads to write a version of the pink letter from the point of view of their respective characters. He used a combination of those four letters in the film.
Usually, bit part players with no spoken lines in this movie are listed in the credits. Normally only speaking parts are listed.