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 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.
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.)
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 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 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.
Joshua Waitzkin is depicted as the next Bobby Fischer in the film and a genius chess prodigy, however the portrayal is immensely exaggerated. Although he became an International Master at the age of 16 (a title which most top players manage to attain much earlier, at the age of 12-14) he never managed to gain the top tier title of Grandmaster. Moreover, the peak Fide Elo Rating he reached was 2480 in 1998 at the age of 22, which was then more than 300 rating points lower than Garry Kasparov who at the time topped the rankings. Last but not least, there are currently (May 2017) 1453 players all over the world rated higher than Joshua Waitzkin and 82 in the US.
Joshua Waitzkin is depicted as the next Bobby Fischer in the film and a genius chess prodigy, however the portrayal is immensely exaggerated. Waitzkin became an International Master at the age of 16 and never even managed to became a Grandmaster. Although gaining such titles was much harder in the era Bobby Fischer was playing, he actually became an International Master at the age of 14 and Grandmaster at the age of 15.
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.