Hisoka, a Monster Clown with a rather disturbing, pedophiliac take on the Blood Knight trope. He can do all kinds of creepy faces, his creepiest is by far is when he prepares to kill a participant in the Hunter Exam.
The Phantom Troupe in general. A band of nigh-unstoppable killers who take whatever they want, when they want, and usually just kill everyone in the vicinity, even if it isn't necessary.
One of the members, Shizuku, is an adorable bundle of Moe tropes. In her second appearance, she's bashing heads into paste without even changing her expression. She also has a creepy looking Living Weapon Vacuum that can suck anything that isn't alive.
Chrollo in general is creepy as all hell, wandering into the Uncanny Valley from time to time. A few of the nen abilities he's stolen are disturbing as well, like the "Indoor Fish" that devour human flesh, only the victim is unable to feel anything, and is kept alive as long as the fish are active (the victim used to show this ability off was Laughing Mad while down to half a head and random bits and pieces of body parts before he was killed.)
"Oh, this looks like a happy, relatively innocent series, doesn't it?" Then the Hunter Exam starts up and people start dying horribly.
Some of the things Illumi can make your body do with his needles are...unpleasant.
The entire Chimera Ant arc is the kind of grade-A Nightmare Fuel that horror movies are made of. Giant Mix-and-Match Critters swooping in and effortlessly butchering entire populations (by the hundreds. Daily,) dragging whoever they don't kill back with them to have the flesh stripped from their bones and turned into giant meatballs for their queen (while they're still alive, mind you.) If you're lucky, you'll get reincarnated as a Chimera Ant and continue the cycle, possibly on people you used to know.
And then the end comes along, with Nightmare Faces galore, and Gon becoming very, very intense and pragmatic (to the point that he's willing to kill an innocent girl.) For anyone who still remembers the old Gon from before all the hiatuses, it can be very unnerving.
The Chimera Ant King. Just the way Togashi writes and draws a character who starts out as all-powerful and nigh-unstoppable and only gets more powerful from there is terrifying.
The Royal Guards are no slouch in this department, either, both in-universe and in Real Life, but especially Neferpitou. One character catches a glimpse of his nen from the floor below him and is so horrified that his hair goes white and he refuses to fight anymore.
Then, there's Menthuthuyoupi, whose power is pretty much weaponized Body Horror, allowing him to grow multiple arms and gain hundreds of eyes as he gets angrier, making him look like something out of a Lovecraft work. His final form is the apex of his weirdness, resembling a grotesque centaur with a giant, deformed face in place of his shoulder.
The anime manages to make some of this worse, not only because it shows some of these things in motions and with sound effects, but the sudden art shifts that accompany some of these things make it absolutely terrifying.
Gon's Tranquil Fury at Pitou, which is very disturbingly subdued compared to how much he usually gets enraged over the tiniest things.
Alluka. Creepy black eyes aside, when she grants an especially large wish, her demands for the next person to come along are severe. And if you refuse her demands four times, something happens, and you, your closest loved one, and possibly many other random people are killed.
Chapter 341 gives us a good look at some of the things that have happened to people trying to enter the Dark Continent. People who entered not only didn't survive, but had their bodies twisted horribly and were thrown back into the human world. According to records kept of what lies in the new world, there are many more horrors to look forward to.
The Kakin Royal Family. Prince Tserriednich is the kind of guy whose hobbies include collecting body parts (like the Scarlet Eyes) and murdering young women as twisted performance art.His expression when he thanks God for the opportunity to murder his siblings so he can inherit the throne rivals Hisoka's and Illumi's. His eldest brother Benjamin, first seen wrestling a lion and breaking its neck in a fit of rage after Tserriednich hangs up on him, is no better. Their father the king's goofy character design belies that he's the kind of man who would order his own children to battle to the death on an expedition to a Death World for the right to succeed the throne. His Nen guardian (which is based on his personality) is a horrific mishmash of insect parts and breasts. And this is the ruling family of one of the most powerful nations in the setting.