At the beginning of the film, when Jim's father (played by Karl Malden) goes into the kitchen to wash up after work, the shadow of the camera can be seen on the far wall. Then a shadow of the boom mic is seen on the wall shortly after that as the camera pans left.
Close-up shots of Jimmy Piersall playing shortstop and right field reveal a low outfield wall backed by trees in the background. These games were supposed to be in Fenway Park, which would have a high left field wall and bleachers in right field.
Piersall is show wearing uniform number 37 immediately upon his promotion to the Red Sox. During his first two years, and part of a third year, he wore uniform numbers 24, 26, 2, and 34, not donning his well-known number 37 until partway into the 1953 season.
When Jimmy Piersall is taking the field in his high school state championship game, he's wearing #37. When the team is in the locker room after the game, another player on his team is also wearing #37.