Charlize Theron - who had been a model before becoming an actress - had publicly vowed never to play a model onscreen. Woody Allen was aware of this and wrote her a letter specifically asking her to change her mind about that so that she could appear in his film.
According to Allison Janney, neither she nor Allen knew the proper pronunciation of the word "triplex". After she did two takes pronouncing it as "try-plex", Allen told her to find the right pronunciation. She decided to ask real estate magnate Donald Trump who was on the set preparing for his cameo. Trump told her it was "trip-lex" and that is how she pronounces it in the film.
Cinematographer Sven Nyquist had lost much of his sight at the time of filming. Allen would describe the scenes to Nyquist so Nyquist could tell Allen how each scene should look. This partially became the basis of Allen's blind director in Hollywood Ending (2002).
Allen wanted to hire Kenneth Branagh for the lead role but was unsure whether he could pull off an American accent. As Branagh was filming The Gingerbread Man (1998) at the time, Robert Altman screened most of the film for him, and Branagh got the part.
In the scene where Leonardo DiCaprio and Kenneth Branagh are watching a boxing match, magician David Blaine can be seen sitting behind them. Blaine was on the set visiting DiCaprio that day and they put him in at the last minute.
Joe Mantegna's character Tony Gardella asks his family "what am I Don Corleone?" It's worth noting that Joe Mantegna played Joey Zasa in The Godfather Part III. Zasa was awarded control of the Corleone Family business in New York. This is before Zasa fervently tried to have the Don Corleone killed.