In the final game at the end of the movie, the opposing team is constantly referred to as the Giants when their uniforms clearly show them as the Cardinals.
In the climactic game, Farrell hurriedly dons an over sized uniform. However, in his final at-bat, a long shot from behind the plate shows him in a uniform that fits him perfectly.
When Joy E Brown is playing pool, when they switch to view above the pool table, the person shooting has bare arms, Joe E Brown is with long sleeves. ALSO when Joe E Brown is making the last shot to pocket 5 balls, only those 5 balls are left and Joe E Brown is standing near a corner pocket. Next thing we see is the shooter (Joe E Brown) shooting from a side of the pool table.
The plot hinges on the lights being turned out at the Chicago Cubs' ballpark during a night game, so the hero can change into a uniform. Wrigley Field, the Cubs' home field, did not have lights installed until 1988.