Throughout the movie the Olympics are only implied. The word "Olympics" and the Olympic symbol are not actually in the film due to strict control by the Olympic Committee.
Real-life Olympic gymnast and medalist, Dominique Moceanu, has a cameo is the film. While she is not a native Ohioan, Moceanu has lived in Northeast Ohio much of her adult life and currently resides in the Cleveland area. The film is set in Amherst, which is a suburb of Cleveland.
All of the eatery locations in the film are real places (Hastee Tastee, Quarry Cafe, Midway Mall food court). Hope's house is on the small street of Brandt Avenue, but the building used for Pavleck's gym (once a pizza parlor) was demolished in 2016.
In order to avoid potential claims of infringement of Olympic trademarks, the names of the cities given for the competitions in the movie for 2004 and 2016 were Rome and Toronto, while the 2004 and 2016 Olympics were held in Athens and Rio de Janeiro, respectively.