Continuity mistake: When Billy finally finds his mom and talks to her in front of her apartment, the door behind her changes from (almost) fully closed to much more open, to an intermediate state, and fully closed again at the end. (01:25:30 - 01:28:00)
Continuity mistake: At the beginning after the car skids on the road and stops on the left side there are trees and snow but not the road, however the truck hits them on that side.
Continuity mistake: After Billy catches the bus, argues with Freddy and leaves, the floor around the people besides it is dry, then wet, repeatedly.
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 Billy drops his notebook into the garbage can in the bathroom, it's open to the final page with his mom's possible addresses on it. But, when the other kid finds it, it's closed.
Continuity mistake: Before Billy hits the bus with the lightning the floor around the stairs is wet but the floor below is dry and has the sun on it.
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.
Continuity mistake: When the robbers enter the supermarket and start shooting Billy, in the following shots Freddy's distance from Billy changes, appearing closer in close up shots.
Continuity mistake: In Freddy's notebook of Billy's powers, the way they are written and crossed out changes. For example, when he writes and circles "Fire Immunity", the lines through "Laser Eyes" are different.
Continuity mistake: In school, Billy nags about being hugged by the little girl. She says 'sorry' and a girl with a pink backpack walks by. Then she vanishes and a shot later she reappears and walks by again.
Continuity mistake: When Billy mimics a phone call to Shazam in front of his school mates, there's a boy with a blue jumper on the left who stands up and leaves. When the shot changes he is sitting down and stands up again.
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.
Continuity mistake: When Billy drops the truck at the school the sun changes between shots.