Although in real life Lou Gehrig batted and threw lefty, he wrote with his right hand (likely a victim of "correction," as was the custom back then). In the film, he writes with his left hand.
Eleanor tells her story to writer Joe Durso while sitting in the new, renovated Yankee Stadium, which opened in April 1976. However, "My Luke and I," the memoir on which the film was based, was published in April 1976, so it would have had to have been written earlier -- meaning if Eleanor was interviewed at any time in Yankee Stadium (highly unlikely, since it was under renovations in '74 and '75), it would have been the old Stadium, not the new one.
When Eleanor moves to New York in 1933, she says the Yankees were on their way to another pennant. The Yankees didn't win the pennant in 1933.