Roberto Benigni's line "It's a sad and beautiful world" was the result of a misunderstanding. The script read "That's sad and beautiful music", but Benigni said "It's a sad and beautiful word", but Waits and Jarmusch misheard it and though he said "WORLD", and so, the line stuck.
Jim Jarmusch had intended that the shack that the fugitives find refuge in after escaping prison would have bunk beds, so as to make it look exactly like the prison cell. Incredibly, they found a shack where two bunk beds were already standing, so no extra furniture had to be added.
Nicoletta Braschi plays the Italian woman in the film whose character's name is Nicoletta. The actress was born in Cesena, Italy and the character she plays was also born in Cesena. Her character in the film plans to marry Roberto Benigni's character named Roberto. Five years after the film was released, Nicoletta Braschi and Roberto Benigni marry.
Down by law is dedicated to Pascale Ogier and Enzo Ungari. Both unexpectedly passed away a year before Down by Law was released. Pascale Ogier was a French actress, who died at the age of 25 of a heart attack after an overdose. She had starred in "Full Moon in Paris" (1984), for which she posthumously received a Cesar award. Enzo Ungari was a writer, who wrote several screenplays for director Bernardo Bertolucci, one of which was "The Last Emperor". Enzo Ungari passed away at the age of 37.
Zack says he previously worked as a DJ at stations WWOZ, WHLO, and WAKR. WWOZ is an FM station in New Orleans, where the film is set. WHLO and WAKR are AM stations in Akron, Ohio, where director Jim Jarmusch grew up. Now featuring mostly talk and news, they were Akron's two most popular music stations in the 1960s when Jarmusch lived there.