Unclear whether this is a bizarre coincidence or inside joke, but when the character played by Natalie Wood is taking a taxi home from the abortionist, it passes a large billboard mentioning New York Mayor Robert Wagner. Robert Wagner, of course, was also the name of Wood's former (and future) husband Robert Wagner.
In the opening scene, the booking agent asks Rocky if he "wants a wedding," meaning does Rocky want a paying gig. But the question "do you want a wedding" also foreshadows what Rocky struggles with later in the film.
In the opening scenes of the movie you hear Rocky Papasano's full name called out over the loudspeaker just before he meets Angela in the crowd. Papasano is a made-up Italian surname, but in Japanese "papasan" means Mr. Dad.
The Rossini family is ethnic Italian. Angie Rossini is portrayed by Natalie Wood, who is ethnic Russian. Dominick Rossini and Julio Rossini are portrayed respectively by Herschel Bernardi and Harvey Lembeck, who are both ethnic Jewish.