Brian De Palma couldn't find the right girl to play Veronica. Rebecca Romijn convinced him that one of her friends, Danish model Rie Rasmussen, would be perfect for the job. He met her and signed Rasmussen because he loved the way she walked.
Melanie Griffith convinced husband Antonio Banderas to take the role of Nicolas Bardo, even though it wasn't the lead. She did it as a favour to Brian De Palma, who had given her her big break in films decades before with, respectively, Der Tod kommt zweimal (1984) and Fegefeuer der Eitelkeiten (1990).
Antonio Banderas didn't really see himself as the character Bardo. But he wanted to learn directorial skills from Brian De Palma. He shared this thought with De Palma, who agreed to teach him everything he wanted to know if Banderas took the part.
The underscore music (by Sakamoto) that plays through most of the initial heist is an obvious tribute to (or parody of) Ravel's Bolero. The rhythmic ostinato is the same as in Ravel's piece, and the orchestration is remarkably similar. All that's been changed are the actual melodies.
John Stamos: Rebecca Romijn' then-husband is uncredited as the "cheesy agent" who contacts Nicolas on the phone.