The music instrument that Vladimir Ivanoff (Robin Williams) played was a saxophone. Robin Williams spent months learning to play the sax and apparently according to his music tutor, got to a level of accomplishment that would normally take a student two years.
In preparation for his role, for about a year, lead actor Robin Williams studied Soviet customs and learned the Russian language. Reportedly, Williams spent five hours a day learning Russian and had learned to speak it well within a month. By the time of principal photography, Williams was at a proficiency level where he could carry out a conversation. William's teacher was a Russian actor called David.
Appearing in this film was Russian actor Saveliy Kramarov who was a real life defector from the USSR. Kramarov had appeared in over 40 Russian films and was given permission to immigrate to the USA in the early 1980s. Kramarov gave up his Russian film career for small parts and religious freedom in the United States. This was Kramarov's first American movie and ironically he played a KGB agent.
The grandfather of the film's director Paul Mazursky was born in Kiev, Russia. In 1905, he defected from Czarist Russia by jumping a Russian train troop. Mazursky's grandfather met his grandmother whilst immigrating, when traveling on the boat bound for the USA.
One of the movie's main movie posters featured a long preamble that read: "America is sometimes a strange place even for Americans. Let alone for Vladimir Ivanoff, a Russian defector with a black roommate, a Cuban lawyer, and an Italian girlfriend. Who's learning to live with Big Macs, cable TV, hard rock, softcore, unemployment and a whole new wonderful word for him. Freedom."
One of the film's main movie posters which was an aerial view of New York City was the subject of a successful civil lawsuit from artist Saul Steinberg. Steinberg sued alleging that the movie poster infringed the copyright of his renown 1976 ink, pencil, colored pencil, and watercolor on paper "View of the World from Ninth Avenue" illustrative cover of the 29/03/1976 edition of 'The New Yorker' magazine [See Case: Steinberg v. Columbia Pictures Industries, Inc., 663 F. Supp. 706 (S.D.N.Y. 1987)].