Other mistake: Towards the end of the film when they're at the fair, Mary refers to the Sins as "sins", but there is no way she would know that they are sins.
Suggested correction: If you think about it, Billy shouldn't have known either. However he does posses knowledge of these after he transforms and receives the powers. It is evident that when the other children held the staff and said Shazam to get the powers as well, that it also came with some, at least limited, knowledge of these things.
Agreed, except the scene I'm referring to takes place before the rest of the family get powers.
She called them "sins" before she held the staff.
He does get told they are sins.
Mary may not have known but Billy would, because old Shazam talked to Billy about how a previous champion released the sins into his world.
Other mistake: Shazam catches the bus and everyone's fine. But really, how is him catching the bus at a dead stop 6 feet off the ground any better than it hitting solid ground a fraction of a second later? He's not magically cushioning everyone on the bus.
Other mistake: All the kids at the foster home are of very different ages, but they all go to the same middle school.
