Peter's mutation is depicted as pretty intense, giving him a nasty fever and showing his DNA mutating. Obviously, he's just going to get cool spider powers in the end, but knowing this all came from a mutant bug bite gives the scene a mild Body Horror vibe in the moment while it's happening.
The birth of the Green Goblin. His costume is close to Narm, but when it's just Willem Dafoe grabbing Dr. Strom and sending the poor man crashing through the window and into some equipment, then making a psychotic facial expression before letting out a primal scream, it's terrifying.
Made worse by the fact that we're told later that Strom died. We only see him get thrown into a shelf. The force could conceivably be enough kill him, but a lot worse probably happened considering Norman ends the scene by grinning in the direction he threw Strom and leaping off camera to do God knows what.
In the scene where Harry finds Norman passed out, we get a quick flashback of his transformation into the Green Goblin in the form of an extremely effective Jump Scare, showing him struggling in the transformation chamber with his eyes rolled back into his head.
There's another, even more effective, jump scare later in the movie when an uneasy hug between Norman and Harry is interrupted by Peter dreaming about the Green Goblin coming to get him, shrieking. Peter is only just out of high school, and dealing with a sadistic super-villain like the Goblin is clearly taking its toll on him.
Peter himself is quite terrifying when he's hunting down the carjacker that killed Uncle Ben. He first lands on the killer's car, punches a hole right through the top of it, and grabs his face (and later breaks the car's windshield as well). But it gets even worse when Peter confronts the carjacker in the warehouse. He appears out of nowhere and brutally attacks him, smashing his head into glass multiple times as well as twisting and breaking his wrist with little effort. The sheer terror the carjacker expresses towards him just before his demise really says it all.
Moreso after Spider-Man 3 reveals that Dennis Carradine here isn't the actual shooter, but Flint Marko is.
The Green Goblin decides to interrupt a parade, whereby he terrorizes Mary Jane. Just before doing so? He vaporizes the Oscorp board of directors into skeletons and then into ash with a single pumpkin bomb. On-screen.
Norman hallucinating that the Green Goblin is laughing and talking to his reflection in the mirror.
Norman: Where are you?
Goblin: Follow the cold shiver running down your spine.
The depiction of Norman's Sanity Slippage in general. By the very end, there's almost nothing of the old Norman left, just the Goblin.
The Green Goblin sets a trap for Spider-Man by setting an apartment building on fire. As Spidey is rescuing a kid, the Goblin lures him back inside by playing a soundbite of a woman screaming then throws a blanket over his back so that Spidey doesn't realize it's him until he gets up close. When he does surprise Spidey, he plays the soundbite of the screaming woman once more for surprise value.
We see him arming a pumpkin bomb behind his back when he's saying "Are you in or are you out?" Between that and his "You're pathetically predictable! Like a moth to the flame!" when he first reveals himself, he almost certainly used one of those pumpkin bombs to start the fire in the first place. Which is supported by the fact that the fire obviously spread very quickly by the time Spider-Man showed.
For Aunt May, a quiet moment of prayer is interrupted by the Green Goblin crashing into her bedroom and make her finish the assurance of pardon. For Peter, the realization that not even his beloved aunt is safe from his archnemesis must have been a shock.
The next scene with Peter rushing into May's hospital room is just as bad, too.
"Those eyes! Those horrible yellow eyes!"
Peter is worried about Mary Jane and calls her house to make sure she's okay, but instead of Mary Jane, he gets the Green Goblin on the other line, who giggles and says in a creepy sing-song voice, "Can Spider-Man come out to play?"
Green Goblin presenting Spider-Man with a Sadistic Choice: save Mary Jane or a Roosevelt Island Tram car full of passengers.
Green Goblin's beatdown on Spidey (though it turns from scary to awesome when Spidey gains Heroic Resolve and then completely turns the tables on the Goblin). But it starts with the Goblin blowing a Grenade at his face that blows half his mask off and leaves him a bloody mess and proceeds to become the most brutal one-on-one fight scene in superhero films until The Dark Knight Rises between Batman and Bane.
For the part in the fight where the Goblin has the advantage, theres no music at all. Which somehow makes it all the more frightening.
His threat to Peter in this moment, saying that if he had let Mary Jane die before her death would have been quick and painless, but now he's going to go back and "finish her nice and slow." It's made scarier because his mask's eyes have opened up and we can see Norman's actual eyes, glistening with malice. And if you look close, you can see Norman Osborne has a Slasher Smile as he says this.
Goblin: You've spun your last web, Spider-Man. Had you not been so selfish, your little girlfriend's death would've been quick and painless. But now that you really pissed me off, I'm gonna finish her, nice and slow. MJ and I...we're gonna have a hell of a time!
The entire wrestling match scene, right up until Peter wins, is extremely troubling. Unless you understand the kayfabe going on, the league comes off as a sleazy Blood Sport where contestants sign their life away with a legal waiver (and management doesn't seem to mind a teenager stepping in), the sadistic crowd is absolutely loving the violence, and Bonesaw is apparently willing and able to seriously injure his opponents with very little effort.
Wrestler Preceding Peter: (being carted away on a stretcher) My legs! Oh God, I can't feel my legs...
"Corralled" and "Scorpion's Rampage." The first? You have to protect the poor guy from a swarm of similar drones - which are also after you. And the second? He finally snaps from Paranoia and goes Ax-Crazy on you; and while you can't help but pity him, he's nevertheless a JuggernautThat One Boss with all sorts of Madness Mantra quotes. Oh, and he ultimately escapes without a word - making him the only antagonist with no resolution. By the way, enjoy the music in both missions.
The stealth levels in Oscorp. The first one is very dark with creepy music playing. If the guards or cameras catch you, the entire area goes into alarm mode, sending out the robotic Super Soldiers. If they find you, they will fire at you with everything they've got.
The unlockable test animation of Vulture getting into position for his heist with Shocker. It's not a very action-filled piece, with Vulture riding a subway train as he inspects a robotic spider drone he's taken from Oscorp, mumbling to himself. But the music combined with the early 2000 visuals makes it feel like a feverish mix of "encountering a sketchy person on an actual subway at night" and "meeting the Tall Man from Phantasm.