In the scene in the room where the live coverage of game one was being announced, after all the men had left the announcer states the final score. However, instead of saying the "Reds" he says the "Red Legs". This is inaccurate because Cincinnati was not called the Red Legs until the 1944 season.
In the scene before the first game in Cincinnati, Buck Weaver and Kid Gleason are talking at home plate in the empty ballpark. Buck (John Cusack) is swinging a Louisville Slugger. While the bat is probably an older one, it clearly has the "Powerized" label on it. Louisville Sluggers did not have this label until 1931, 12 years after the 1919 World Series.
In Charles Comiskey's office after word of the scandal is out, Comiskey's lawyer is bouncing an autographed baseball in his hand made by Rawlings. During the Black Sox scandal, A.L Reach was the official ball of MLB.
Early in the film, there is a close-up of Eddie Cicotte's right hand (Strathairn) as he is preparing the ball to throw his famous "shine ball". On the ball, the logo " Rawlings", as in the Rawlings Sporting Goods Company, can clearly be seen. But in 1919, Major League Baseball exclusively used baseballs manufactured by Spalding. Major League Baseball would not switch to baseballs made by Rawlings until 1977, 58 years later.
In one scene, Dickie Kerr tells manager Kid Gleason that he remembers the first ball game he ever went to - Gleason pitches a no-hitter to beat Cy Young 1-0. Gleason stopped pitching to become a full time infielder in 1895. Dickie Kerr was born in July of 1893, so it is unlikely that he would remember seeing Gleason pitch. Gleason pitched for St. Louis (Kerr's home town) in 1892, 1893, and 1894, so it's possible Dickie did attend the game, but remember it, probably not.
Judge Kennesaw Mountain Landis elected 1st baseball commissioner on November 12, 1920. The scene directly following the announcement of his commissioner-ship shows a newspaper date of January 14, 1920, 10 months earlier.
The end of the film leads you to think that Chick Gandil's career ended with the official banishment of the "Black Sox". Actually, Gandil sat out the 1920 season because of a salary dispute with the Chicago White Sox.
Fred McMullin's role in the scandal is completely incorrect as shown in the film. McMullin overheard the conversation between Chick and Swede in the locker room, not in the bathroom. While McMullin was a friend of Swede's, he was only included out of fear he'd tell Gleason about the fix. And the conversation took place in August of 1919. McMullin earned his $5,000 by grounding out in game 2 with catcher Ray Schalk is scoring position. MvMullin later served as a liaison between the gamblers and the players, whom were forced to throw several key games during the 1920 season out of fear of being exposed.
During the trial, Buck Weaver exclaims that he batted .327 in the series. Actually he batted .324. The .327 probably came from a researcher's haste: Weaver's lifetime world series batting average was .327, but he batted just .324 in the '19 series.
In an overhead shot of the field before the conversation between Weaver and Gleason the day before the World Series opens, there are obvious remains of the lining for a football field. Cincinnati had no football team at the time that would have played at Crosley field.
In game 7 of the World Series, the scoreboard in the background says that the Cincinnati Reds scored their only run in the bottom of the sixth inning, but in actuality they scored that one run in the bottom of the fifth inning.
During the first game of the series, the scoreboard is shown in the bottom of the 4th inning with the score being Reds 1, White Sox 0. The actual box score shows that the Reds scored one run in the bottom of the 1st inning and the White Sox scored one run in the top of the 2nd inning. The score should have been tied 1-1 at the bottom of the 4th inning.
When Joe Jackson signs his confession he does it with an X. Joe Jackson, though illiterate, could sign his name by mimicking a pattern. There are autographed baseballs and photographs from the time that prove this.
When the players meet the lawyers for the first time, the head counsel introduced his co-counsels by likening them to famous ballplayers (i.e.: "The Ty Cobb of lawyers"). One of the Sox players asks, "Who is the Babe Ruth?" The head counsel replies "I am". In the time line of the film, however, which is suggested to be between the 1919 and 1920 seasons, Babe Ruth would have just completed his final season with the Boston Red Sox, and also was his first season playing more than 100 games, and he might not have been as famous as he became later. However, the actual indictments of the players (and the meeting with the lawyers) took place after the 1920 season. In 1920, the Babe had by far the greatest offensive season ever, being the first player to 30, 40 and 50 home runs in a season, as well as setting a slugging percentage record that stood for more than 80 years.
Cincinnati is the first team shown batting in Game 1, despite the fact that they are the home team. However, in the preceding scene, when Rothstein first arrives to listen to the play-by-play, the announcer can be heard reading off the results of Chicago's turn at bat in the top of the first inning.
While "The Star-Spangled Banner" was not officially made the official national anthem of the United States of America until 1931, it was sung during the first game of the 1918 World Series and had been popular for years, so it's reasonable for it to be sung before a 1919 game.
Some of the neighborhood kids are listening to the game on a "crystal set" radio. Although the first "real" radio station in the USA (KDKA in Pittsburgh, Pennsylvania) wasn't launched until 1920, less well organized broadcasters were operating as early as 1909. It is not inconceivable that an enthusiastic local was broadcasting details of the game and so, whether accurate or not, it seems reasonable to allow artistic license.