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.
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.
Other mistake: All the kids at the foster home are of very different ages, but they all go to the same middle school.
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.