Just the whole concept of it. It's like Oz meets Elfen Lied meets more insanity.
Episode 1: Exactly three minutes into the first episode you get to see a classroom of middle school kids mutilated into shredded corpses covered in glass, concrete, and their own dismembered bones and blood. And then you see Mimi's bloadsoaked head clutched in the Red Man's hand like a trophy... with the most horrified look on her face. What does that imply? She saw the whole thing and begged not to be killed. But the Red Man found it more pleasing to his sick gullet to just put her out of her misery.
And then comes the trial. Not only is Ganta a helpless little kid under the mercy of an iron-fisted court, he has nobody with any moral fiber to defend him. On top of that, he's seamlessly impersonated and incriminated with evidence he's an insane killer. After panicking at the sight of everyone ready to convict him, he looks like he's lost his mind... which of course, causes the grief-stricken parents of the victims to think he has no remorse (for a crime that wasn't even his doing), and beat the hell out of him. Next, his corrupt bastard lawyer deserts him and he gets a life sentence. Then, of all things, he gets egged. Finally, he's placed in a jail that can only be described as Satan's playhouse. Think you're having a bad day?? Like hell you are compared to this shit.
It gets worse when it is later revealed that Shiro was the one who set up Ganta to go in prison. Not only that, but Shiro is the Red Man. So, Ganta befriended Shiro and arguably loved her, just to find out she liked him back enough to ruin his life and put him in Deadman Wonderland.
And it turns out that Shiro knew exactly what she was doing.
The dog race from episode 2. The fact that the audience were watching real people die, and convinced themselves it was all an act.
In the anime, a woman asks her boyfriend how he can watch it. He replies that it isn't real, BUT EVEN IF IT IS, IT'S STILL PRETTY COOL, "'cause they are criminals."
Shiro as a little girl having her arm fall apart and trying to put it back together.
If you have a little sister, niece, daughter, etc. do not, do NOT watch Shiro's backstory.
Speaking of the Carnival of Corpses, the entire idea is similar to the dog race, except that it's a one-on-one match between contestants. The preview shows a woman having her arm ripped off as she screams in agony. This is directly followed by a man having his face stomped flat. Also, if you lose, you are tortured simply for losing. Crow has his right eye gouged from his head.
On top of that, look at the machine! It spins around like a gambling machine, flashing several options such as hand, tongue, stomach, etc. Do they remove those, too?
Deadman Wonderland. The entire show is based off the manipulation of your own blood as a weapon, for starters. And then, we have Shiro, the wretched egg who maniacally goes about slaughtering people: their remains take the form of decapitated bodies, mutilated half forms, with blood everywhere, and random body parts, vividly drawn with accurate detail. Let us also recall Toto, who mimics others' Branch of Sin by eating/sewing on body parts to take on their blood! Or how about when Toto took someone's head, and then proceeded to jam his arm up it, and make it a puppet.
Not to mention that the Mother Goose system, which exists to prevent Shiro from killing herself, is largely made up of cubes full of her body, the collection of which is largely to blame for her insanity.
Chapter 53: Hagire's death. He totally got what he deserved, but boy did La Résistance brutally curbstomped the crap out of him.
Speaking of which, the Wretched Egg returns by stealing and destroying the heart (key to keeping the Mother Goose system operational). Her chilling smiles and laughter don't help at all.
Chapter 55: All the remaining questions regarding Shiro's backstory are answered. As the Wham Episode trope on the main page says, the answers are as bad as you think it is.
Not least of which is the truth behind Shiro. There is no Split Personality, never was. The real Shiro still loves Ganta, but she is also livid and resentful toward her childhood friend for being able to live the happy life she never had. This not only adds loads of complexity to Shiro, but also makes her a rather disturbing character to watch in hindsight.
The true purpose of the Mother Goose system. Yes, it does limit the powers the Shiro could muster. However, the real purpose of the system is so that Shiro will always regenerate and thus never die (as the aftermath of the Great Tokyo Earthquake reveals). Because Sorae (Ganta's mother) grew too attached to Shiro to see her die, Sorae had condemned the poor girl to continue being used as a lab rat for even more dehumanizing experiments.