In the second half of the movie where Josh's father brings him back to the park to play with Vinnie, real-life Josh Waitzkin and Vinnie (both much older than actors playing them) are visible in the background.
The character of Jonathan Poe (Josh's young rival) was based on real life young chess prodigy Jeff Sarwer. In the National Primary Championship which the climax of the film is based on, Josh and Jeff actually tied for first place, after which Josh won on tie-breaks. While Sarwer would go on to win the World Championship Under 10, he soon disappeared with his sister and father; the family was known for living a travelling lifestyle (no permanent adress, etc.)
The film's star, Max Pomeranc, was chosen because he is in real life a chess player (or was at the time of the film). The producers wanted someone who would be at ease and "correct" playing chess. None of the film's other stars played chess in the beginning, but eventually Joe Mantegna learned.
Most of the characters who were famous chess players were actually played by themselves (Joel Benjamin, Roman Dzindzichashvili). The one exception is Asa Hoffman. The real Asa Hoffman did not like the way he was depicted in the script (he is shown as being neurotic, when the book describes him as being quite self-aware), and refused to cooperate, so he was played by Austin Pendleton.
The chess piece that Josh finds in the park at the beginning of the movie appears to be a replica of a knight from the Isle of Lewis chess men, the earliest chess pieces found in Europe, dating back to the 12th century. Harry and Ron are seen playing with similar pieces in Harry Potter & the Sorcerer's Stone.
The real Bruce Pandolfini is very different from the character Ben Kingsley plays. Pandolfini is actually a Brooklynite with a mustache, glasses, and curly brown hair, and he is reported to have a very friendly, soft-spoken demeanor. In fact, Pandolfini can be seen in a cameo role in the movie; he is a kibitzer when Ben Kingsley goes to see Josh in Washington Square; thus, Pandolfini tells "Pandolfinni" that Josh is a "young Fischer." Josh Waitzkin is quick to point out that the portrayal in the film is fiction, and should not be confused with reality.
The trivia item below may give away important plot points.
The final game, specifically the endgame position, was composed for the movie by Josh Waitzkin and Bruce Pandolfini (the real-life game ended in a draw, and no one saved the score sheets). In the October 1995 issue of Chess Life, Grandmaster Larry Evans states that the position is actually unsound; Jonathan could have actually won the game.