Jude Law learned to play the saxophone and Matt Damon learned to play the piano for this film. Damon's training enabled him to recreate the proper keyboard fingering; however, the music heard in the film is played by Sally Heath (the Bach) and Gabriel Yared (the Vivaldi).
Fausto and Dickie (and Tom, later) sing "Tu Vuo' Fa' L'Americano," a humorous song about an Italian man in the 50s who wants to imitate the American lifestyle he sees in the movies. But American food doesn't do him any good and in the end, the money he spends comes from his mother's purse.
Is based on the novel of the same name by Patricia Highsmith. There are an additional four novels which follow "The Talented Mr. Ripley", they are "Ripley Underground", "Ripley's Game", "The Boy Who Followed Ripley", and "Ripley Under Water".
As noted, the opera excerpt is a scene from Eugene Onegin, by Tchaikovsky. The title character in the opera is, like Ripley, an attractive, charismatic, and clever young man, who aspires to be accepted by people of a higher social standing. This is best portrayed at the beginning of the third act when Onegen crashes a dinner party where he is clearly over his head and is quickly spotted as a poseur.
The opera shown on the film is the end of Act II from Tchaikovsky's "Yevgeny Onyegin." In this particular scene, Lenski challenged his friend Onyegin for a duel over Olga, who had been engaged to Lenski at that time. Lenski was mortally wounded, and Onyegin departed Russia for a self-imposed exile.
John Malkovich remarked in an interview with the BBC that he came close to directing "The Talented Mr. Ripley," and that he was in negotiations to obtain the rights to direct a remake of the first "Talented Mr Ripley" adaptation, Purple Noon (1960). Malkovich later played Tom Ripley in Ripley's Game (2002).