When Walter tells Sister Francesca that he'll "do anything to help" the orphanage after the fire, he has tears in his eyes and his hands clasped together in front of him. In the next shot, his eyes are dry and his hands are at his sides.
In the closing scene on the staircase, when Walter tells Henry about the adoption, Walter's hands are together in front of him with his elbows on his knees. In the next shot, Walter has his left hand at his side and his right hand behind Henry.
When the little kid at the orphanage is reading the post cards from Walter, he says they have been through Kentucky, but later on in the film we see them passing through Kentucky.
When Eddie is watching Walter's fight in the temple, Eddie's yarmulke falls off as he is getting excited. It is back on his head in the next scene
Sister Francesca is clearly wearing lipstick. Nuns are forbidden to use cosmetics.
When Henry is watching the YouTube video of Walter beating up Mad Milton's father, he is logged on to the same account (Eddie's account) that the video was uploaded from.
There are a couple of fights where you can see that the fighter doesn't come close to actually hitting his opponent. One in particular is when the Eddie and Walter are watching a fighter kick his opponent, who drops even though one can cleanly see the kick wasn't even close to his head.