Now, another thing before I begin: I do realize the game already has supernatural elements, and more to come, but the ones already established mainly involve the Darkness, and are a little too prevalent in it to be considered mysterious. The Darkness, from what I understand, is meant to be a Pilgrim’s imagination/paranoia, essentially, which becomes more and more active as he explores unknown territory. However, my ideas essentially assume that there are, in fact, supernatural creatures in Salem's world, and they’re more than just ‘imagination'. Thus, some could be spotted/discovered outside of the Darkness.
Many of these ideas are just for flavor and atmosphere, and won’t actually affect the gameplay too negatively. They aren't supposed to be pains in the ass, and they're also supposed to be rare when it comes to sightings. Part of the charm of supernatural entities (whether real or not) is the mystery surrounding them. This mystery, of course, would be lost if, say, a ghost appeared next to you every weekend asking where the beer is.
Slenderman

Anyone who’s been on the internet knows who/what he is to the point where he might not even be scary anymore to some. Though if that’s true, a playthrough of his games might change their mind. He may want his 20 dollars, but he’ll get it from you by stabbing you through with tree branch and then going through your pockets.
Anyway, the Slenderman is, of course, a modern-day creation, and not one of legend. The suit he wears wouldn’t really fit the setting. Luckily for us, the internet has gladly provided images of Slenderman being a creepy ******* throughout history, with attire to fit the time period, such as in the image above. Yes I know that that's more of a Victorian-era outfit, but you get the gist. Besides, Slenderman's always bringing sexy back no matter what you dress him in.
In the game world of Salem, there would only be one Slenderman entity. Once every two days or so, he will teleport to a new area. Stemming from his teleportation point will be a circular area of temporary Darkness. However, this would have limitations. Slenderman's purpose is to provide something scary to run into if you venture too far from any sort of civilization. This means he wouldn't be able to spawn too close to Leantos or settlements. This would also keep newbies from being screwed over.
His Darkness would work the same way any other Darkness does. Creatures that normally spawn it would spawn in it, though they would disappear when the Darkness is lifted. Slenderman himself, once he teleports to a new area and creates said Darkness, will then teleport to another location within his darkness every two minutes, but he will be invisible most of the time. We'll get back to that later. Inside the darkness, as a tribute to the Slenderman games, a series of notes can be found, etched onto the side of rocks.

Discovering all of these notes will allow a person to craft a valuable inspirational, probably something that can give a high amount of Cloak and Dagger points. It doesn't really matter, as long as there's some incentive for a person to go into Slenderman's darkness.
Because there's also a risk.
As stated above, Slenderman will be invisible most of the time. The only way a player could be able to tell where he is could be provided by a heart beat noise or something similar. The closer you are, the faster the heart beat. However, due to Slenderman's random teleportations, it'll be hard for his location to be pinpointed. If you draw too close to his current location, he will suddenly appear. This will coincide with your usual Slenderman stuff, maybe a VGUI effect that red-shifts everything, and of course, some terrible sound. You'll need to draw away from him pretty quickly, as he'll lower Blood and Black Bile at a rapid rate while you're too close. Once you 'escape' from him, he'll randomly teleport once again. Finding all of his notes will be a mini game in itself, though if you lose, you'll be knocked out. Naturally, this means if you drop anything, you're gonna be venturing back into Slendy's territory to get it back.
The only place safe from encountering Slenderman is actually in the real Darkness. Slenderman does have a habit of appearing in the daytime, after all

Oh, and he's also completely copyright free!
The Dover Demon

This creepy ***** was spotted only once, and in New England, not doing anything in particular save for being a creepy *****. He's said to be an alien, or a ghost, or an alien ghost, though he's likely just a hoax. Still, who gives a *****? It's all in good fun.
The Dover Demon, in Salem, wouldn't really be more than a flavor element, much like the Dryad seen in Haven in Hearth. It would not affect to gameplay too much. Like Slenderman, there would only be a limited amount of entities in the world at a time, in his case two or three. Like Slenderman, these entities would teleport to random locations, and once again, fairly far from settlements. If a player were to encounter one, the Dover Demon wouldn't likely let him get too close. Instead, he'd instantly book it in the opposite direction before teleporting to a new location a few seconds later (mainly to prevent the awkward scene of him running headfirst into a tree). This would give the impression that it's a creature that can only be seen out of the corner of your eye.
But there's no way it'd be worth to code him/make a model for him if it was just that.
There would be a way to get something out of him. If a player were to stand completely still right after spotting it (and you'd need pretty damned good hand-eye to do this, even if you're zoomed out using Ender's client), the creature will not run. Instead, it'll simply face the player, as if it's examining him. However, you would be allowed to load a gun/ready a slingshot or whatever, but shooting him would be a mistake.
Upon being attacked, the creature would immediately teleport away, but not before attacking with a blinding (if VGUI permits) telekinetic strike. This would likely involve some sort of screeching/unpleasant noise as well, and would completely drain a player of their Black Bile.
However, if the player chooses not to attack it, and holds still for about fifteen seconds, the creature will actually grant you a reward for being such a chill cat. Before teleporting away, it'll grant a buff that will raise your inspirations at twice the normal rate. Because let's face it, after seeing this *****, you'd figure anything would be possible.
Native American Ghosts

Stories of Native American ghosts were common in Colonial New England, especially after numerous (deadly) skirmishes between the pilgrims and them. Ghosts in general were a reality to many people, even more-so than today, where it's reported that 1/3rd of all Americans believe in them (and probably need to check their plumbing, but hey, anything's possible).
Unfortunately, unless I'm mistaken, my particular idea about them probably wouldn't be able to be integrated until the next world. It would involve a new terrain type, though it'd be very similar to a confectioner forest. The usual trees and critters would be within it, but with the addition of a new dead tree that would help with atmosphere. And of course, there would be ghosts in it, because let's face it: it'd be cool to be able to tell somebody in game, "Avoid heading North, that forest is haunted."
The ghosts of the forest would be largely invisible most of the time, like Slenderman above, and wander about randomly. When seen, they'll look like regular players, with normal animations (not hovering about or transparent and all of that). They could be running, or maybe even shooting and reloading a musket, forever fighting their last battle. Naturally, they'll be wearing Native American attire. They would only appear in flashes if a player is near, but off-screen, perhaps they could be seen on the mini-map as 'player' once and a while, keeping people away from them for the most part. The point is they're supposed to be fairly hard to encounter directly. The whole forest, however, could have a passive, creepy, ambient soundtrack, and the ghosts themselves could emit Indian hollers and stuff like that with a hint of reverb.
However, you can get something out of ghosts. After unlocking the Theology skill, one will be granted access to a new stance, 'Put to Rest'. If this stance is active near a ghost, it will force it to appear and stand still. This will rapidly drain Black Bile, but if you're able to keep it refilling long enough, the ghost will eventually dissipate, finally getting a chance to go to heaven/hell/Mars/somewhere besides our ****** plane of existence. However, it will leave behind a small gift, an inspirational/ingredient, ectoplasm (or something more original and prettier sounding, hopefully). Ectoplasm can be used to grant a heft amount of Faith and Wisdom, or can be used to craft a new type of potion, one that would do something awesome like granting you temporary, 30 second invulnerability. It doesn't matter, as long as it's proportionately awesome to how hard it is to encounter and then Put to Rest these ghosts, which I hope would be pretty damned hard.
Signing Off
Anyway, that's all for now. Hope my ideas will be considered, but if not, I still had fun thinking them up. I'm sure others have similar thoughts to this, so post away! I'll be doing so myself once I do more research on New England monsters/cryptids.
However, before I go, let me leave you with this:
https://www.youtube.com/watch?v=bqlHdPlHK_s
You're welcome.