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.
Continuity mistake: Young Billy has brown eyes while teen and adult Billy have blue eyes.
Suggested correction: The "Adult Billy" isn't really an adult Billy, that is how Dr. Savana would've looked if he hadn't tried to take the Deadly Sins Ball. So the adult Billy figure is the default figure for anyone who passes.
All of his brothers and sisters are older versions of themselves (by both gender and ethnicity). It's not like Darla would have looked like Shazam had she been deemed worthy first. I could understand if you meant that they might not have all the characteristics (after all, older Freddy does not need a cane so eye color could be different) then I could buy that but older Billy is not the default for just anyone.
Suggested correction: While I don't think it's expressed in the film, much of the film mirrors Shazam from the comics (mid 80's and up). I didn't see anything in the film to suggest it's what Dr. Sivana would have looked like or a default setting. In the comics, Shazam represents Billy's idealized self, not Billy as an adult. Same for the other kids. In the film, and comics, Billy also retains his adolescent personality to further indicate he's not an older version of himself.
Continuity mistake: When the Sivanas' car is landing there is a "blink and you'll miss it" moment where we see the front of the car and its window is flat when it lands but in the next front shot the window has been bent fully forward.
Suggested correction: I'm sorry but if you have to pause to see it then it's not a valid mistake.
Trivia: Spoiler: At the very end of the movie, Superman makes an appearance at the school cafeteria. He is referenced many times throughout the film.
Suggested correction: How is this trivia? It's obvious in the film.
Some stuff like this is interesting to read about even if you've not seen the film yet. I didn't know that scene existed, for one.
Continuity mistake: Before Billy gets in his mom's apartment, it's daytime, but when he flies away it's night.
Suggested correction: When he leaves the sky is dark but not as dark as it comes to be later, at the carnival, which means it was just getting dark at the time, it didn't change all of the sudden.
He talks to his mother for less than ten minutes so there would still be light.
Could have been a while between going there and gathering up the courage to actually knock on the door. Just a thought.