Factual error: In the coffee shop when Roy Hobbs is having coffee, there is a Coca-Cola sign in the window featuring the "fishtail" logo used between roughly 1957 and 1961, not the time period portrayed in the movie.
Factual error: In the final game, the Pittsburgh manager calls for a left-hander in the bottom of the ninth inning. The pitcher strides to the mound, Roy takes his stance in the batter's box...and no warm-up pitches are taken. I understand that a pitcher isn't required to take warm-up pitches, but no pitcher who throws smoke would be willing to cut short his career just to get the game over.
Factual error: After the Knights clinch a tie for the pennant and are celebrating in the clubhouse, Hobbs tries to call Iris on a pay phone that is of early 50's vintage. The movie was set in 1939.
Factual error: Presuming that when the Knights are playing the Cubs at Wrigley Field in Chicago, the stadium never had an upper deck above the right field bleachers in its history.
Factual error: The national anthem, which is played before an afternoon game in the movie, was not played before major league ballgames in 1939. That didn't start until 1941, and wasn't done by all major league clubs until 1942.