Other mistake: In the last game, Chet pitches six innings ("You gave me six great innings!"), then Henry takes over pitching, meaning he'd be pitching in the 7th inning. Sounds good, until we fast forward to the 9th, with Heddo batting with two outs... Assuming Henry was perfect, Heddo would be the 9th batter Henry faced, meaning he would've been Chet's last out in the 6th, which of course he wasn't (the Chet play at the plate ended the 6th and he wasn't facing Heddo.) Also, Heddo was seen walking up to the plate after the second out of the inning (the rundown at second base), with Martinella saying something like "holy goosebumps, it's Heddo" as he approached. Heddo would've been on deck, so it wasn't a surprise, plus he would've already been at the plate prior to the rundown play.
Suggested correction: There is a reasonable explanation for both of those points. Heddo could have been a substitution player after the sixth inning, or be a pinch hitter, so hadn't been to bat yet. This would be logical since Heddo is a fastball hitter and they think Henry is still throwing fastballs, so as a last ditch sent him in. For why they didn't notice that Heddo was on deck, they were captivated by the on-field action, and with Henry off the mound going over by first base and doing stupid stuff, hadn't looked over yet to see who was next.
Other mistake: Rudy continually checks the roster to see if he made the dress list. The captain of the team is Roland Steele; the first one to visit the coach about giving up his jersey for Rudy. Every time Rudy looks at the list he scans past the last names for "S" where you should see Steele, Roland. Steele doesn't appear on the dress list yet he dresses every game. Stock, J. (Capt.) appears on the list, so Steele should too.
Other mistake: When Benny signs the autograph for the fake baseball he signs it Babe Ruthe with an 'E' on the end. This can be seen when Smalls put it back in his step dad's trophy room.
Suggested correction: He did though it's apparently supposed to happen like that as one of the boys says "Baby Ruthe?" when he's signing it and a comment is made about how bad it looks. Strange as it seems; this appears to have been done purposefully for the movie thus would not be a mistake if that's what the actor was directed to do.