The Reveal of the Winter Soldier's identity and Cap having to fight him. It's no wonder why he goes into shock upon finding out. Imagine your best friend that has supported you your whole life, was there when tragedy struck and when you were bullied, and who now doesn't even remember who you are, wants you dead, and will do the act personally.
There's something unsettling about how, when Cap first sees him with his mask off and calls him by his name, the Winter Soldier just growls "Who the hell is Bucky?" in a tone that makes it clear he genuinely doesn't know what the heck his target is talking about.
Arnim Zola's present day form as a vast computer inside what's supposed to be a munitions storage facility at Fort Lehigh, especially the way he appears on the old screens and his reveal of HYDRA's grand plan.
The way he talks with a slight echo and his face jerking up and down. Then, as a missile heads to obliterate him, Captain America and Black Widow, he talks calmly about his own approaching death. Bear in mind that this is a man who, seventy years prior, was a coward that sold out HYDRA to save his own skin.
The police ambush of Nick Fury. The fact that all of those "cops" were sent to take him out prove just how deadly and serious HYDRA is about people meddling with their plans.
Nick Fury being injured at all can be pretty damn distressing, given his Magnificent Bastard tendencies usually mean he's on top of everything, and comes out unscathed.
The Stinger, featuring Quicksilver and Scarlet Witch in Von Strucker's custody, not quite sane and continuously using their powers, ending with a quick shot of Wanda using her magic destructively. Speaking of insanely powerful things in the hands of evil, did you ever wonder where Loki's scepter went? Von Strucker has that too.
A lot of the elements of the Winter Soldier's character and treatment are pretty horrific in general.
The electroshock therapy that Bucky is subjected to, in order to wipe his memories of Captain America.
Not to mention his flashbacks to everything that happened since his "death" as Bucky, and his transformation into the Winter Soldier. A brief moment in the flashback shows more of Bucky's arm being amputated, from his point of view. They did that without anesthesia, or worse, they used anesthesia and Bucky's enhancements meant it didn't work. The fact that all of the flashbacks are POV shots makes them extra creepy.
Of special note is that when preparing for his memory wipe, he calmly opens his mouth to accept the bit he's given. He's been subjected to this torture for so long that he simply accepts it as if it were normal, despite the fact that it's incredibly agonizing physically (and likely emotionally). This behavior is either instinctive or conscious, depending on whether or not the memory wipes actually erase the memory of previous wipes. Whichever is the case, it provides more nightmare fuel: Either Bucky remembers every horrifically painful memory wipe (he was under Hydra's command for at least half a century, so who knows how many times the procedure has been done) and has essentially given up and willingly submitted to the process, or he doesn't remember them, but there have been so many of them that his subconscious has been trained to accept it without resistance.
The Winter Soldier's theme on the score. It starts subtle and quiet, and builds into an distorted industrial cacophony culminating in what sounds like a scream of terror. This not only reflects the reaction people who know what he is have when fighting him, but also what it feels like to be, somewhere in Bucky's real mind.
The Winter Soldier showing up in Pierce's house, sitting in the dark, not saying anything, and barely even blinking is creepy in its own right. Then you realize Pierce is in on it, not a target. Then the housekeeper shows up and gets shot by her employer, not the Soldier, with no more reaction than "I wish you'd knocked" and a mildly regretful sigh. Cue Oh, Crap! moment.
Almost as bad is how everyone elsereactstohim. Any time anyone besides Rogers goes up against him, they lose. Badly. And it barely even seems to slow him down. Natasha's brief battle with him just pisses him off and ends with her being shot. Anybody that tries to fight him, like the S.H.I.E.L.D. launch personnel and the Quinjet pilots, just gets taken out quickly, efficiently, and without a single word from him. The Winter Soldier is as close to the Terminator of the original movie as the MCU has come yet.
Despite him being in league with HYDRA, Agent Sitwell's death is pretty shocking, especially with how we've come to known him in the Marvel One-Shots and previous films. It just happens so suddenly and without warning. Sitwell is in the backseat of the car that Steve, Natasha and Sam are in, when the Winter Soldier comes out of nowhere, grabs Sitwell through the window, and flings him screaming into the other lane of traffic, only to be struck and reduced to pieces by an oncoming truck.
When Steve Rogers arrives home and sees Nick sitting in the chair. Nick's appearance after escaping the police and Bucky is far from pleasant. He looks drained of energy, tired, and incredibly weak. The sight is just chilling.
Black Widow's face when chased by the Winter Soldier in the bridge scene. She's terrified on the brink of panic. The implication of how terrifying the Winter Soldier is comes when one remembers that the only other time when Black Widow had a similar reaction was when she was alone with the Hulk, trapped in the bowels of the Helicarrier in The Avengers.
Pierce activating the security badges placed on the World Council members, which ignite and burn through their chests, killing them. Then threatening to do the same to Natasha.
Some of the deaths that Bucky carries out, such as tossing a man into a jet turbine or shooting a guy in the throat, leaving him to die an agonizing death.
Natasha's line, "Everyone we know is trying to kill us."
The villains' grand scheme combines multiple strains of contemporary popular technophobia, from anonymous, inescapable drone assassinations to "big data"-scale privacy violations, all at the behest of an uncaring computer in the hands of equally uncaring and corrupt authorities.
The Insight carriers targeting millions of people... including a man who might very well be playing ball with his son.
Insight gets even worse the more you think about it—it constantly tracks everything about you that's online and issues the kill order the moment you demonstrate a pattern that it believes will become a problem for HYDRA somewhere down the line. Meaning that it's entirely likely that after the initial saturation fire, they were going to be picking off high school kids...
Sitwell even mentions a valedictorian being as valid a target as Bruce Banner and Stephen Strange.
...And that satellite running the analyses is still out there. And they're watching you.
Sam mentions that his wingman Riley was hit with an RPG, while flying the Falcon suits. Think about what Riley looked like afterward.
Music-wise, the Winter Soldier's Theme, especially its first half, is just plain unsettling, starting with something that sounds like a woman screaming in an empty hall, going through grinding mechanical noises and then something like engines powering up and a variety of industrial sounds that, with ambient background, are just plain creepy. Not a thing to listen to if you're alone in the dark.