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!"
There is a conversation between the kids at McDonalds about whether or not Batman eats fast food and one of the kids says it would be hard to imagine the Batmobile going through the drive thru. The very next year, Batman himself references going through the drive thru in the opening moments of Batman Forever (1995).
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 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)
In one scene Thomas Heywood talks to Billy about Pitcher Walter Johnson. Johnson pitched for the original Washington Senators, who would relocate to Minnesota and become the Twins in 1961. In addition, an extra can be seen wearing an old Washington Senators baseball cap.
The one game playoff between the Twins and Mariners lasted twelve innings. In 2009, during their last season at the Metrodome, the Twins actually played a one game playoff which would last twelve innings. Interestingly that was also a season during which the Twins owner (Carl Pohlad) died and left the team to family members.
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.
Thomas Heywood was depicted as being very similar to Carl Pohlad, the real life owner of the Minnesota Twins at the time of the film. This includes both holding large financial fortunes. Poland owned the Twins from 1984 until his death in 2009, after which family heirs took inheritance of the team.
The trivia item below may give away important plot points.
Near the end of the film, Randy Johnson of the Seattle Mariners enters the one playoff game to relief pitch. Coincidently, the next year, he entered a one game playoff against the Angels near the end of the game to relieve.