All About Eve was made in 1950, which means that it couldn't be shocking if it wanted to. Due to the Hays Code, a morality code for Hollywood pictures, there was very little "mature" language, hardly any implied sex, and definitely no nudity.
That keeps All About Eve strictly in family-friendly territory even though it's way too sophisticated for a younger audience. Addison is a little creepy and controlling at the end, but we're not sure if his motivations toward Eve are sexual in nature. We see one shot of Eve in a towel, but it's done in a tasteful, modest way. Back then, that's about as shocking as it got.