Rated PG, Casablanca was meant to do many things—thrill, inspire, provoke emotions of heartfelt sympathy—but not to shock. There's no surprise shower scene halfway through. No creatures pop out of Ugarte's chest. It's just not that kind of movie.
The rating was assigned due to mild violence. By today's standards, really mild violence. A couple guys get shot, or shot at, but no visible blood is ever spilled. No one stumbles across the scenery with their intestines leaking out of their abdomen. Ah, well. Maybe in the sequel.