Arturo Sandoval and Dizzy Gillespie did in fact perform together as depicted in the film and it was Gillespie who helped Sandoval and his family defect and the adjustment to being in the United States soon after.
Singer Gloria Estefan, who plays Mia Maestro's friend in the film, has in real life had Arturo Sandoval play on some of her albums.
The seaside park scenes showing wrought-iron fences were shot in the Parque de Palomas (Pigeon Park) in Old San Juan, Puerto Rico, while the black and white film the character of Dizzy shoots is actually footage of Havana, Cuba.