When Henry has to take his first AB (against the L.A. Dodgers), the pitcher in that scene (Tregoraw) is Tim Stoddard. Stoddard was a technical adviser for the baseball scenes in the movie. Coincidentally, Stoddard was actually a pitcher for the Cubs in real life, he pitched on the '84 Cubs team that won the NL East title (and eventually lost to the San Diego Padres in the NLCS).
John Candy, as the radio broadcaster, is uncredited. His role isn't mentioned in the movie credits because he wasn't originally cast in the movie.
When Henry's mother (Amy Morton) is celebrating Henry scoring a run after being walked, she hits her head on the lamp hanging above her (at around 57:45 mins). Morton obviously didn't mean to do this: she is visibly hurt and after sitting down mutters "oh... shit" (at 57:49, which is dubbed out on the audio, you have to lip-read).
Except for once, Martinella gets Henry's last name wrong. He calls him the following: Rulingfurter, Gardenhoser, Raviboozer, Rosinbagger, Runnamucker, Rowengartner, Rulengruder, Rosenburger.