In the climactic scene with Ken Griffey Jr. getting thrown out due to the hidden ball trick, the play is factually accurate. Bowers, the pitcher, had stepped off the rubber before the throw. Because he stepped of the rubber, he did not need to throw the ball. He would not have been called for a balk.
John Gordon, who played broadcaster Wally Holland, was the real-life voice of the Minnesota Twins until he announced his retirement after the 2011 season. While his use of silly statistics (e.g. batting average against left handed pitchers faced at home for the first time in the last month of the season) is a parody, he did use his trademark home run call when he said "Touch 'em all, Mickey Scales!"
In a movie in which the plot revolves around the owner of a baseball team passing away, in this case Jason Robards as Minnesota Twins owner Thomas Heywood, it's ironic that the film unintentionally features a reference to a real owner who had passed away. During the Twins games against the Texas Rangers (when Billy argues with the umpire), if you look on the sleeve of the Rangers' gray jerseys, there is a black "HEC" stenciled into the uniform. It's a reference to H. Eddie Chiles who passed away shortly after selling the Texas Rangers franchise to an investment group led by Dallas businessman Rusty Rose and future President of the United States, George W. Bush.
In addition to the numerous real life major league players who make cameos in the film, the Twins shortstop, Pat Corning, is also played by a real major league player, Kevin Elster. Elster played for the Mets (1986-1992), Yankees (1994-1995), Phillies (1995), Rangers (1996 and 1998), Pirates(1997), and the Dodgers (2000). Statistically, his best season came in 1996 with the Rangers when he batted .252 with 24 HRs and 99 RBIs.
In a film that contains many references to baseball history, the most subtle is that of the Twins pitcher named Mike McGrevey (Scott Patterson). In the early 1900's in Boston, there was a saloon keeper with that name who led a group of Boston Red Sox fans called the "Royal Rooters". (Today, they would considered a "fan club")They would enter in a large procession and sit in the lower left field stands of the old Huntington Ave Grounds (and later, Fenway Park). The Rooters, who were often drunk, were known for viciously taunting opposing players and playing music throughout a game with a marching band that accompanied the Rooters. Their biggest claim to fame in baseball history came in the 1912 World Series when they became so disruptive that they delayed Game Seven of the Series. The Red Sox eventually won that World Series in Eight Games (Game 2 ended in a tie and was called for darkness, forcing the Series to go beyond 7 games)