When Clark first enters the spaceship (essentially the Fortress of Solitude, but it's also a spaceship) he finds a mostly-decayed skeleton.
The viral TV spot of Zod's message to Earth is pretty chilling.
The prelude to the actual message is in itself nightmare fuel. The lights go out and only the TV works, and there's this strange, ghostly screech coming from it, and it goes on for at least half a minute as it steadily rises in this awful, metallic violation. For a moment the film turned into a horror movie.
Ma Kent certainly thought so. When the power flicks back on, she practically jumps out of her skin.
Faora: You will not win. For every human you save, we will kill a million more.
Superman appearing to be sinking in a mountain of skulls. It's only an implanted vision via Zod's Mind Probe, but the threat it represents is very, very real.
Before that happens, we see Superman cough up blood and collapse to the ground, while Lois desperately shouts for the uncaring Kryptonians to help him. After, he wakes up Strapped to an Operating Table, with a Torture Technician drawing blood from him.
The Tornado sequence, especially after the recent tornado outbreak in Oklahoma.
Clark watched his father die. He watched Jonathan Kent's body get swept up and ravaged by the harsh tornado winds. Pray he was denied from seeing the body after it was found...
So... how many people lost their lives as result of the World Engine? Plus Kal and Zod's fight?
According to this, 129,000 confirmed dead with another 250,000 likely dead, meaning that 379,000 people died in the crossfire.
Holy shit! Seven-hundred-fifty Billion dollars worth of damage done to Metropolis and the other side of the world, with a two TRILLION dollar worldwide impact. For comparison, The Avengers, another awesome, but highly destructive film clocked in at one-hundred-twenty billion dollars of damage. It's a bit distressing that the next installment will take place during a worldwide economic depression.
Just imagine the ways people would have died in this film: crushed by the debris, caught in fires and explosions, falling from God-knows-how high up—hell, even the tornado scene doesn't guarantee that everyone on that road made it to the underpass. And then there's death by the World Engine. You know, how Jenny, Perry, and Steve could have died had Superman not destroyed the opposite Engine in time.
How the battle plays out and all the sheer destruction really hits home that this is a much more real-world approach to Superman. When this kind of action happens, its not all bright and heroic and everyone manages to get to safety and people have time to cheer their heroes on. Its manic, horrifying, and outright catastrophic. The attitude during this a far cry from most other comic book action hero films where this is usually the triumphant moment of fighting back. Now Superman knows he can't drag any fights of this scale into Metropolis...or anywhere with a civilian population for that matter until he learns to make even better use of the powers he has.
Consider this about the World Engine. As part of the terraforming process, it's explicitly stated to be increasing the density of the Earth's core, which it's doing for the entire time until it's stopped. The long-term ramifications of this tampering are never fully revealed, particularly since the process was interrupted before it was completed. Particularly chilling is that similar tampering with their core is what destroyed Krypton.
The gravity effects are explicitly shown to expand from their central points. We watch in horror as cars are lifted up, then crushed - not by the fall, but by the enhanced gravity. And while we don't see it as graphically, people running from the pulses are shown being dragged down by the effect.
The destruction of Krypton. Bonus points for Lara watching it without her husband.
Young Clark's out-of-control senses give the poor kid some very nightmarish moments; seeing walking skeletons and floating, working internal organs, while hearing loud, unbearable noises coming from all directions.
To an ordinary human it all looks like a little boy having a psychotic break!
Even short of a psychotic break, for viewers who have themselves experienced sensory overload/similar difficulties (minus the x-ray vision hopefully) that part of the film was hard to handle. (Even more so granted that the film's extreme loudness and the destructiveness of its fight scenes made those same sensory sensitivities freak out.)
It also looks a lot like a panic attack to some.
Not to mention all the unintentional Fridge Horror that comes with those powers, thinking of just how far those senses could go. Fridge Horror and Squick combine when you think he could see the full effects and symptoms of cancerous and/or sick people, unborn fetuses (YMMV on whether this is disturbing to see), or hell, anything that can count as Body Horror.
It then gets cranked Up to Eleven when Zod and Faora have their life support systems forcibly removed in the final showdown. Clark had a whole lifetime to adjust. Zod and Faora spent most of their lifetime in the Phantom Zone, and thus took much longer to adjust to Earth's environment and their newfound powers. It's strongly suggested that it takes Zod up until the World Engine docked in Krypton is destroyed, roughly 16-20 minutes (of elapsed time). And the high-pitched-whine that Clark experienced is made much more intense when we are forced to experience Zod's and Faora's adjustment through their point of view, to the moment that, despite all the terror they have (theoretically) or will about to cause, you can still feel their pain.
Zod's flashback: Being freed from the Phantom Zone... just because those who imprisoned you have been vaporized in a planet-wide cataclysm, and being forced to watch, despite what you thought were your best intents, your home planet tearing itself into oblivion and being unable to stop it, spending the remainder of your years space-hopping from Kryptonian outpost to Kryptonian outpost only to be greeted by (what is strongly suggested) to be centuries-old Body Horror.
Supes' flashbacks to when he was a child. Anyone who has been bullied can relate to this greatly.
Zod declaring he will kill all the humans just to spite Superman. "If you care about these humans so much, then you can mourn for them!"
Superman breaking Zod's neck. Even he is traumatized by this.
Made even more traumatizing by the fact that by his own hands he killed the only other living Kryptonian in the galaxy, excluding the ones trapped in the Phantom Zone. Kal-El is not only the last Kyrptonian, he made himself the last.
Lois falling toward Earth in an out-of-control escape pod. That begins to burn up from the atmospheric re-entry.
Tor-An grabbing a pilot and ripping the man apart so that he explodes into fine red mist. It's a very brief shot but that doesn't mean it's not a shock.
The fate of Zod's followers. They are trapped inside the phantom zone without an intact ship or cryofreeze to protect them. And recall that Kryptonians in this continuity can starve... eventually.
The implication that there might be concentrated Kryptonian particulates in the air now...Kryptonite might be a ways from making it to Earth after the explosion, but who says a genius can't make use of something like that...
It's potentially worse. We see Zod's ship pull in a massive amount of debris from Krypton when it engaged it's hyperdrive, so depending on whether that debris continued to piggy-back in their wake as they searched for Kal-El, some of it possibly might have ended up in Earth orbit.
The process inflicted upon Zod and his followers as they're sent into the Phantom Zone. It looks like dark ice rising up and consuming them, and also looks VERY painful; some of them cry out in agony as the ice reaches their heads, even the stoic Faora.
The droning sound that the World Engine and Zod's ship makes. Made more horrifying by the gravity effects that the sounds indicate.
Faora's style of fighting (combined with her dark attitude) is sometimes both this and awesome at the same time.
It's more understated than other examples, but there's the Codex, the source of life for Kryptonians, originally being located on the incomplete skull of some long-dead, forgotten Kryptonian. Especially when it becomes Fridge Horror later on: when Zod told Superman that he would rebuild Krypton on the latter's bones, it wasn't a metaphor.