Continuity mistake: In game 154 in Baltimore where Maris needs 2 home runs to tie Babe Ruth's record, he comes to bat in the 2nd inning. The scoreboard shows that the Yankees have scored 1 run in the inning. Later in the game when Wilhelm comes in to pitch, the scoreboard shows that no runs were scored by the Yankees in the 2nd inning.
Factual error: In the lounge scene after Mickey leaves the table, Whitey says that Mickey was 18 years old when he came up to the Yankees in 1951. Mickey was born in October of 1931, and that would have made him 19-years-old in the spring of 1951.
Continuity mistake: When they are showing clips of Roger Maris in the field, a ball is hit to RF. Roger makes a play on the ball and makes a "great throw" to second. The next shot shows the SS take the throw from "RF" and tag out the runner. The direction of the throw and runner shows the throw came from the catcher, not the outfield.
Continuity mistake: In the scene where Roger Maris and Mickey Mantle are being interviewed right after Frick rules about the separate records, Maris throws the ball, then turns to talk to one of the interviewers, and when he is done talking he throws the ball again. The ball was never thrown back to him in between.