After the manager removes pitcher Eddie Albert at the beginning of the first game of the World Series, Albert is put back into the game so publicity pictures can be taken. The rules of baseball do not allow this.
When asked what the tallest hotel in Kansas City was, a cab driver claims that it was the Imperial Hotel. No hotel named the Imperial Hotel was ever the tallest hotel at any point in the history of Kansas City.
With the movie's time frame established as nearing the end of the 1941 baseball season, Pepita Zorita is selling war bonds. Technically, US treasury bonds were available for sale in 1941, but they were called "defense bonds" as the United States had not yet officially entered World War Two. The bond name changed to "war bonds" after the US entered the war in December 1941, three months after the 1941 baseball season ended.
In the climax of the film, the radio announcer says that the situation in the game was bottom of the ninth, 2 outs with a runner on second base. However, when Wacky makes contact with the baseball and puts the ball in play, the stock footage of the baseball shows the bases loaded.
In a tie game in the bottom of the ninth inning, the stock footage of the baseball game shows that he bases are loaded and when the batter puts the ball in play, all three runners can be seen crossing the plate with the umpire signaling that they are safe. In a real baseball game, the game would have ended once the runner on third crossed the plate and the batter reached first base; there would be no need for the additional runners to score and by rule they would not have been allowed to score.