These are what we call the 'YMMV items.' Things that some people find in this work. We call them 'your mileage might vary' because not everyone sees these things in the same way. This starts discussions in the trope lists, a thing we don't want. Please use the discussion page if you'd like to discuss any of these items.
Complete Monster: Superboy-Prime begins his descent towards the trope here, killing multiple superheroes, and then blaming them for it, trying to kill Superboy so that he can take his place, trying to kill the entire universe so that he can have his world back (though in fairness, it's our world as well), and finally beats Kal-L to death with his bare hands. Some feel that he hit CM status here, others think that didn't happen until the Sinestro Corps War or even Legion of Three Worlds, but either way, by the time the story ends he has crossed the Moral Event Horizon and is heading on down.
Designated Hero: The heroes in the book seem downright psychotic. Where to begin? Superboy jovially freeing the murderous Black Adam to help them despite the justified doubts of a comrade? Powergirl's non-reaction to a man's head being turned into hamburger meat in front of her? Given the premise, these could've been perfect examples of how dark the heroes of New Earth were becoming if they were ever called for these actions. Despite being one of the supposed true heroes, Kal-L doesn't exactly come off smelling like roses, either. When calling out Diana for how the Justice League are acting completely unheroic, one of the key points he lists is how their League "lobotomizes their adversaries" ignoring that Dr. Light had raped Elongated Man's wife, and that the lobotomization in question was an accident anyway (they were attempting to "clean him up"). It certainly wasn't the choice a hero makes, but Supes's complete lack of understanding given the situation doesn't speak well of him. One wonders what his response would be if asked what he would've done if he had just stumbled upon Lois being brutally raped.
Moral Event Horizon: Alexander Luthor has crossed it from before the story started and just kept on going. Superboy Prime crosses it towards the middle by murdering lesser known heroes and at the end by killing Golden Age Superman.
Alex's concrete crossing was probably in the lead-in series Villains United, when he kills Pariah.
They Just Didn't Care: In the second issue, Tempest tells Dolphin to get "their daughter" to safety when the Spectre arrives to destroy Atlantis. Tempest and Dolphin didn't have a daughter, they had a son. This could've just been written off as an editing mistake, but even when the trade paperback collections of the series were released, Tempest's word balloon was never fixed.
It seems someone at DC finally realized the mistake with the latest trade paperback printings bearing the new DC logo, and Tempest now refers to his and Dolphin's "son" instead of "daughter."