The extremely unsettling catacombs inside the giant Monkey head, which are composed of body parts, giant mushrooms and lava. The thing about these is that they randomly generate and form a maze, and you can't navigate them without the Navigator necklace, so if you don't know this you can be going round in circles forever (although it will usually regenerate the room in which you came in after going through a few doors).
The game does a great job mixing creepy creepyness with familiar and funny creepyness. Still, almost everything that happens on the graveyard on Scabb Island happens to be Nightmare Fuel.
Guybrush does one of the most creepy and brutal things in the series himself: He rips off LeChuck's leg
Largo catching you in his room is pretty scary if you don't use the voodoo doll in time. This is echoed in the last part of the game when you have to do the same for LeChuck, except that Guybrush doesn't give you a warning before he bursts into the room..
Rum Rogers Jnr's Basement, in which there is the skeleton of his father in the bath. This is made funny by the fact there's a toaster in the bath (making it anachronistic) but the presence of it is still scary.
The game has one of the darkest sections of the entire series on Blood Island, when you have to investigate the Goodsoup family, especially when you go to the crypt. Blood Island's permanent night has quite a tone of foreboding to it.
The MystesOfTimeMarsh in which you occasionally come across your future self. It's extremely creepy if not outright scary, especially as it relies on memory to complete it (if you get it wrong you cause a time paradox and have to restart this section).
Humorously lampshaded when you melt down the Pyrite Parrot, whose voice slows down, and Guybrush comments that that's a little disturbing.
Less humorous is the Marquis De Singe, who performs amputations on all his patients, no matter how minor the injury, and when Morgan LeFlay breaks his finger, it heals.
He also suffers from a horrible Family-Unfriendly Death, as his turban that is supplying him with his Healing Factor is eaten by moths, causing his wounds to catch up with him. He wearily chases after Guybrush's animated severed hand, which he had been using to fuel his healing, only for the hand to push him into his own wind machine, causing his matter to be broken down and scattered across the seas. His scream cuts off abruptly as the machine spits out his remains like a woodchipper.
Another death, this time belonging to Guybrush himself! While getting run through with a cutlass isn't the most violent death, especially due to the Bloodless Carnage, Guybrush's inability to die due to him being in a LucasArts game, or in this case a Telltale game, has been a small Running Gag throughout the series, so the fact that it actually happened is that much more painful.
The giant manatees, especially considering that they shouldn't even be scary at all.
The absolutely brutal beatdown LeChuck gives Guybrush near the end. He even goes as far as keelhauling Guybrush! (For those who don't know, keelhauling involves tossing a person overboard and dragging them along the underside of the ship by pulling them back out from the other side with a rope.)
LeChuck's fate in The Stinger. All that's left of him is a bottle of green goo with his skull belt buckle floating in it, and he is screaming in agony.
Chapter 4: D'Oro lost an eye offscreen, and apparently he thinks that eyepatches are out of style, so instead he leaves the gaping hole exposed.
Chapter 3: Bugeye's trump card of a scary face involves sticking one of his eyeballs out of his mouth.