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.
Penthesilea starts off with arranging Diana's assassination, which actually ends up killing Hippolyta, her own sister. After that, in Flashpoint #4, the moment Captain Thunder is separated back into his six component children by Enchantress, Penthesilea kills Billy Baston without hesitation. Even Diana herself was stunned by the fact that Captain Thunder was just a child (well, multiple).
The Joker AKA Martha Wayne. She has a freudian excuse but her horrific, sadistic treatment of her child captives (and it's implied this is far from the only time she's done it) take her so far beyond the Moral Event Horizon it's frightening.
Gorilla Grodd is a genocidal mass murderer in this timeline.
General Nathaniel Adam (known in regular continuity as Captain Atom) who is probably one of the worse human villains in the story.
And don't forget Lionel Luthor in Project: Superman # 2: he leaves his son Lex to be devoured by Krypto (whose mind had been tampered with by Subject Zero to get angry) while he runs away to save his sorry hide.
Reverse Flash counts too, although not for his actions in Flashpoint (where he's barely appeared until the final issue). He's been set up as one since his recent origin issue in The Flash.
Ensemble Darkhorse: In terms of the various miniseries. Batman: Knight of Vengeance is the real breakout.
The Flashpoint universe version of Batman/Thomas Wayne himself is the breakout character of the main series with most fans talking about how awesome he is and not really caring much about the main plot.
Frankenstein and the Creatures of the Unknown has been getting alot of praise as well.
Muchhead-slappingensued when the Flashpoint world map◊ was released and people saw that most of Africa is listed simply as "Ape-controlled." Apparently no one at DC thought this might be taken badly when applied to a continent overwhelmingly populated by black people, given the historical tendency for black people to be likened to monkeys and apes in racist propaganda. For the record, "ape" in context refers to Gorilla Grodd, a previously established Flash villain who is literally a gorilla, but the fact that this is the only information we had on the entire continent (besides the fact that a large part of Northern Africa is missing due to the same war that destroyed most of Europe) was the real unfortunate part, and the fact that Batman: Incorporated had done something similar with the "Batman of Africa" (falling into an unfortunate tendency to treat the entire continent like it's one country) a few weeks earlier did nothing to help.
Amusingly enough, the Grodd one-shot actually seems to pull a Lampshade Hanging on the last part since he's pissed that no one cares about what's happening in Africa (though see Broken Aesop for why this falls a bit flat since it's technically his fault).
But whatever merits Grodd's Lampshading gain are then lost by the fact that the only real resistance he faces during his rampage comes in the form of a band of Child Soldiers and... Catman. That's right; the only costumed guy to face down Grodd is a white guy, doing so on behalf of South Africa.
Additionally, a variant cover that was released that showed Wonder Woman holding Mera's decapitated head drew controversy due to its blunt visual (ironically said cover is speculated to be a homage to a similar cover of Crime Suspenstories that was used as an example of bad taste that eventually lead to the creation of The Comics Code).
The Woobie: Superman. He crash-landed in Metropolis as a baby, accidentally killing thousands. Then he spent his entire life locked in a lab where he was no doubt experimented on for decades. Rockets for Krypto & Kara eventually arrived, but from the looks of it, they've faired worse than Kal-El (KRYPTO IS DEAD & A FREAKING SKELETON WHEN BARRY FINDS HIM!!). He has never known any human kindness nor contact and is so skinny & pale from NEVER seeing the sun.
He did have some Human kindness in the form of General Lane who treated him as a son and more than an experiment, and also Kyrpto. But then Krypto was killed after mauling Lex Luthor as a kid, and General Lane was pulled into the Phantom Zone by Subject Zero who Kal helped free, while he protected Lois. He was then put back into the cage by General Adams and told he would live the rest of his life there, only coming out at certain times for tests, while he scribbles a picture of Lois on the ground.
Selina Kyle, Oracle. Almost totally paralyzed from a vicious attack by the Joker, she's unable to even wipe the tears from her eyes as she relives it.
Harvey Dent's son, who gets kidnapped by the Joker along with his sister, then has to watch his sister get killed by Jim Gordon because she was dressed by the Joker. And later, he has to watch the Joker kill Jim right in front of him.
Cargo Ship: Many people tease Spike about Babycakes and how she was his "girlfriend".
Chuck Cunningham Syndrome: Officer Leah Kearns. She "needed some time off" and doesn't come back. When Wordy leaves Greg tell Ed that they're a man down, however, they've been a man down for a while and are now two men down.
Crowning Music of Awesome: The songs that play over the last few minutes of each episode tend to be pretty fitting/awesome. A list can be found here
Harsher in Hindsight: The episode "Good Cop" is about a cop who gets demonized by everyone because he accidentally shot an innocent kid. A year after that, the "murder" of Trayvon Martin, which has been decided in court of law to NOT be a murder, happened.
The series finale "Keeping the Peace, Part 2" is haunting considering that it aired in Canada the night before the Sandy Hook Elementary School shooting in the United States.
That episode may also be harder to watch after the Boston Marathon bombings that occurred a few months later.
Moral Event Horizon: Any time a hostage taker deliberately executes a hostage, most notably Misha Kondrashoff in "The Fortress" and Goran Tomasic (while his wife wasn't a hostage at the time, he shot her in the back, in cold blood).
Also the plane hijackers in "Grounded" where they planted a few of their own among the passengers and when someone tried to be a hero, they shot him down.