Roberto Benigni's rabbit soliloquy was almost entirely self-written/improvisation, based on his own life experiences. His mother actually did raise rabbits.
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, thought he said "WORLD," and so, the line stuck.
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.
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.