The music that Grimm (Jean-Paul Belmondo) plays in Rome is a music by Nino Rota from La Strada (1954), also featuring a clown as a main character.
First time in eight years that Belmondo has not delivered a top 10 hit movie. The last time that happened was 1976.
Quick Change (1990) was not actually the first but the second filmed adaptation of Jay Cronley's source comic-novel "Quick Change". That movie was made and released five years after the first, Hold-Up (1985), starring Jean-Paul Belmondo and Kim Cattrall, which had first debuted in 1985. Geena Davis played the Cattrall part in Quick Change (1990).
Quick Change (1990) was the last adaptation of a Jay Cronley novel for around fourteen years until the French film Nos amis les flics (2004) which was adapted from his novel "Cheap Shot". The first filmed version of Quick Change (1990)'s source novel "Quick Change" was a French film too, Hold-Up (1985), which starred Jean-Paul Belmondo.