The West Wing, which is much darker and more gothic than the rest of the castle.
According to Word of God, Beast hides the carcasses of animals he's slaughtered in there. I.e, because if Belle hadn't come along he would've turned full Beast and, as mentioned below, lose his humanity.
The Beast's first full appearance, when he confronts and drags away Maurice.
This happens in universe for Belle, when she asks the Beast to come into the light to see him properly; as his foot appears her eyes get wider and wider, and when he's fully revealed she's clearly terrified.
The Beast when Belle disobeys him and goes into the West Wing. For the only time in the movie Belle seems to be in danger of actual physical harm from him.
On top of that, the way he yells can be enough to scare a child.
The creepy spidery coach-thing that whirrs like an angry insect hive as it transports Maurice back to the village. You never see this thing again during the rest of the film. It makes you wonder where it's hiding.
The asylum owner in Beauty and the Beast is WAAAAAAY scarier then even the actual Beast himself. Played by the same person who voiced Frollo, and looked like Frollo.
To elaborate: rather than simply transforming into sentient-but-mobile household items, the servants of the castle are still essentially human, but as each day passes, they become more and more thing-like, slowly losing their humanity. It's implied that once they completely become objects, they'll either be dead, or stuck forever as human souls trapped inside immobile, sightless, voiceless items. In this case, the former actually seems like a kinder alternative.
Gaston suddenly stabbing the Beast in the side with a huge Slasher Smile on his face even after the Beast spared his life. If you pause the movie when he's falling to his death you can see skulls◊in his eyes.◊
That's nothing when you take into account the former option for Gaston's death: when stabbing The Beast on the roof before falling off, he reacted while falling to his doom in a very similar fashion to Heath Ledger's Joker when Batman threw him off the roof in The Dark Knight.
Also consider the Beast's death itself, the placement of the wound looks like Gaston stabbed him and punctured his lung (and knowing Gaston, knew exactly where to stab him to do it), which is a truly agonizing way to die.
And among other things, the music preceding that part and leading into it. There's a good reason it didn't appear on the original soundtrack.
The second chase as well. There's a reason that pack is the page image for Savage Wolves.
According to Word of God, Gaston was originally supposed to survive the fall and then get eaten by said wolves in a deleted scene. It was deemed too dark.
One of the villagers plucking Babette (the feather duster). It's the same as pulling someone’s hair.
If you recall that she has a human form as a housemaid, this could be considered the same thing as rape, which is so much worse.
It could be considered rape if you parallel the feathers for a woman's skirt. The chuckling from the villager and Lumiere's reaction add to the effect. Consider that Lumiere probably gave that guy 3rd degree burns which seems a little harsh otherwise.