The entire Prologue and what happens to the Decoy Protagonist. Those familiar with the tropes presented early on may get an unpleasant shock when they realize that this is what it's like to be an NPC. And for people used to being some variant of The Protagonist it is terrifying.
Two of the optional scenes you can find on the fourth day stand out. There's your potential first encounter with Rani VIII, who very casually tries to destroy the school, then comments on how sturdy it is to you. Then there's the scene on the first floor with Shinji realizing something's wrong while Sakura starts speaking very oddly...
The latter may be even worse when you consider that Shinji is really just eight years old: Specifically, his line about "always wanting a little sister, but..."
The latter might be a sign of things in Fate Extra CCC
The creeping horror of seeing the hallways slowly empty of both rude and friendly NPCs alike. If the diminishing numbers at the end of the week doesn't make it clear just how many people are killing and being killed, the increasingly deserted school-grounds will.
The gushing couple on the first floor who decided to participate together. The guy eventually begins to realize that there's no way they can both win, even asking you to 'keep his honey company' if he dies, but the girl remains oblivious and optimistic until they're forced to fight each other and she kills him.
Possible Fridge Horror when you consider that the Moon Cell/Holy Grail's purpose is to observe humanity, and Archer's comment that it may have chosen a high school setting to observe Masters in non-combat situations. The Moon Cell is creator and arbiter of everything within the confines of its Reality Marble and could easily have arranged "interesting" circumstances to observe the results.
That week also focuses on the Master's willpower being necessary for a win: A Master with doubts or conflicting goals will lose. Since they mention the guy's Servant being exceptionally powerful - he was able to brute-strength his prior matches without info or True Names - it's implied that his unwillingness to kill his girlfriend was his downfall.
Li'l Ronnie eating people, including her parents and her young child.
Possible Fridge Horror: Julius' second 'vision' implies his "failure" status - as a result of the surgery, possibly? - means he ages at twice the normal rate, and he'll probably live 'til twenty-five tops. Given how old he appears to be in-world, is he actually Younger Than He Looks?
Those random fragments of stone pillars in the final area, including the pile Twice is sitting on, aren't pillars. They're sarcophagi, housing the representations - or possibly even the literal bodies, depending on how you look at it - of everyone who died in the prior Moon Cell wars, hence why the screen pans across them when he mentions how "this world was buried in a mountain of corpses" before he won. And he's sitting on a pile of them like it's a stack of logs. Plus, note how they're stacked up towards the Moon Cell: Could they be the coffins of those you've defeated? Is the topmost one, for example, Leo's?
On the first day of the third week, you have your first encounter with Assassin, he seems friendly enough, but only the interference of your Servant saves your life. Once you get out, you see Kuzuki (or rather, Julius) watching you. He's surprised that you managed to survive, and decides that you need to be "dispatched". As he moves toward you, you note that "he's looking at my neck". Thank God Rin chooses that moment to make herself known.