Mineta Minoru is a perverted hero in training who lacks any of the traits that the rest of Class 1-A is praised for having; he isn't altruistic, selfless, kind, courageous, heroic, charismatic or anything of the sort, and his reason to try to become a hero is so he can be seen as cool and get girls, not to mention his beyond inappropriate treatment of his female peers. Despite these traits, he keeps being lumped together with the rest of the class as a great hero to be and is treated as one of the good guys.
To some of the fandom, Bakugo's messy morals in the sense he doesn't seem to actually realize that bullying someone and using violence to solve problems is bad, really paint him as a gray moral character that he doesn't truly seem like a hero. Even more importantly, people in-universe believe he is this, which is why the fact he decided to tell the League of Villains to shove their invitation up their ass and didn't go the "Rival Turned Evil" route that looked all but actually written on the wall is all the more astonishing.
Aizawa is seen as this by his detractors. He's a deconstruction of the Sink-or-Swim Mentor, but a lot of people see his methods as either ineffective or downright cruel. He is willing to expel entire classes, and has done so before, should they not meet his standards, and would have done the same to Midoriya had he not impressed Aizawa at the last minute. While it's later revealed that the expulsions were temporary, they still go into the student's permanent record. He repeatedly uses "rational falsehoods" to get the students to work harder, but it in turn just scares the crap out of them. He's so incredibly militant about stomping down on all hope or love for the job for the sake of trying to adapt his class to the harshness of Hero life (read: it may get them killed and "sometimes you can't save them all") that when other teachers arrive the kids look like zombies, so dour he's made them. He tends to miss important details regarding the behavior of his students or punish them when he does notice.* Including: failing to notice Iida signed up to intern in Hosu, where Stain was last sighted (especially considering that someone who made it to the semifinals of the sports festival could have gotten a more prestigious hero agency than Manual's); thinking Midoriya and Bakugo would become Fire-Forged Friends by facing All Might only for their relationship to remain volatile and All Might almost crippling them; failing to notice Bakugo suffered issues from being kidnapped and being made to take a test that replicated the Kamino incident leading to his fight with Midoriya, then punishing both of them for the fight He also perpetuates the controversial aspect of Hero Society by threatening to punish the students for acting without licenses, namely by saying he'd have expelled the entire class outside of Bakugo, Jiro, and Hagakure for either attempting to rescue Bakugo themselves or for knowing about the attempt and not stopping them. Many end up seeing him as both a horrible teacher and a Knight TemplarRules Lawyer in the process. He even mentions that Vlad King, the homeroom teacher for Class 1-B, is a far better teacher than him, as Class 1-B's teamwork is on par with Class 1-A's despite the former's relative lack of life-or-death experience.
Endeavor, as all his heroic actions are less being motivated to help people and more about bringing glory to himself, he's an asshole to pretty much everyone even in casual conversation and he's so obsessed by beating All Might that he abused his wife and children, just so he could breed a perfect heir who would surpass him. For many, his attempts to change for the better are too little, too late.
Amano Jaku from the manga version of Urotsukidoji is an hedonistic, callous, selfish and sociopathic jerkass who only cares about having sex with any woman he sees and feels zero regard for anyone around him. The only "heroic" thing he actually does is saving a baby from being ran over by a truck, though this is only before he heartlessly tosses the baby into the river calling it a waste of time and saying that he hates babies and old people. Thankfully his anime counterpart is much more heroic with a majority of his nasty traits from the manga being left out completely.
Buju from Urotsukidoji III manages to be even worse than Amano's manga counterpart. He is a vile, nasty, perverted and unlikable psychopath who has no qualms about murdering families (including babies) and raping women and likes getting drunk in his spare time. Even after his supposed "redemption", he's still pretty much the same as he was in the beginning. For example in Urotsukidoji IV, instead of saving a female character from being raped by a demon, he chooses to watch instead as he says he enjoys seeing women getting raped. The only thing that prevents him from being absolutely irredeemable is his love and protection for his adoptive daughter, Himi. Though it still doesn't make up for his despicable personality.
Digimon Adventure tri.: The DigiDestined, unlike in the original series, edge themselves towards this trope. Despite the digimon rampage going on, they'd all rather spend their time focusing on teenage angst and mundane activities like telling scary stories or going to the hot springs. Their treatment of the 02 kids only solidifies their image as this, prominently when they actively cheered on when they destroy Imperialdramon. It's only at the end of Confession that they finally start acting like heroes, and even then it's only to find their missing digimon partners after the reboot, making them come off as self-centred jerks who only act heroic if the problem directly concerns them.
Dominion Tank Police: There really is little quantitative difference between the cops and the crooks. Both prefer to drive large, destructive vehicles, and both cause massive amounts of collateral damage to life and property; one side merely has the advantage of legal sanction for their acts, while the other's motives are purely mercenary. This is most clearly lampshaded in the sequel series, wherein Anna and Uni are allowed to make a HeelFace Turn without the least change to their personalities; they've reformed because they're tired of being chased by the police and have realized that being cops would allow them to continue blowing stuff up, but also provide a steady source of income.
In the first Dominion Tank Police, there is an exchange between squad leader Brenten and Lovelock that illustrates this mentality perfectly. Brenten, probably the next most gung-ho member of the squad besides Leona, and most definitely a dyed in the wool veteran of the squad, suggests to Lovelock that they should quit the force right then, and go off and become criminals, for the action, the money, and the lack of regulations that plague them as Tank Police. From the tone of voice, it's clear that he's saying this in a half joking, half not manner, suggesting that if Lovelock had agreed to this, they would have actually left for a life of crime right then. When Lovelock declines, Brenten immediately recants everything he said, and nothing more is ever said of it again. Dominion is not a serious series, and the fact that the so-called "heroes" are just as bad as the "bad guys" (and sometimes worse) is part of the joke.
Drifters has this in a real bad way. If not for the fact that the enemies they fight are even worse, protagonist Shimazu, Oda, and Nasu would definitely be the bad guys. Within three volumes of their introduction, they've turned the formerly peaceful elves into their own vicious, revenge-focused personal army.
The title character from Nadia: The Secret of Blue Water also qualifies. She's moody, distrustful, bad-tempered, and suspicious about everything. But she's also a Not Good with People sort of person who has never socialized with anyone before except animals. As such, she is unable to recognize how she feels about anyone. As a result of Jean's love, however, she is gradually transformed by the end of the show and uses the Blue Water's power to resurrect the latter when he is killed by Gargoyle.
Fushigi Yuugi's Mayo Sakaki. A Clingy Jealous Girl and walking factory of Kick the Dog and Shoot the Dog moments. Becomes a Karma Houdini because the writer expects us to sympathize with her, despite everything she pulls, and is even thanked by the people she spent all of Eikouden mind controlling or trying to kill. She'd be a Villain Protagonist except that the author insists she's just an ordinary, lovesick girl who didn't understand the circumstances she was in.
Kio Asuno of Mobile Suit Gundam AGE is a rare instance of this trope with a nice character. He was initially sympathetic, being a Child Soldier raised by his vengeful grandpa to see Vagan as inhuman monsters before meeting with them and sympathizing. When Kio decided to stop killing, however, he also stopped even defending himself in battle. His wingmates told him repeatedly this put them in danger as well as himself, and every enemy he spoke to told him to shut up, but Kio ignored this and continued doing the same exact thing every battle. He also bartered away the Gundam's secrets to the Big Bad, which destroyed his side's major advantage. Nevertheless, the show sided completely with his point-of-view as though there was no middle ground between genocide and Suicidal Pacifism.
Gokudo plays with this. From the beginning, the title character is an unlikable ass who uses anything thrown his way to cheat and steal, but everyone always tells him he's the hero of the land. After the first few episodes, he's tricked into killing the Big Bad. Eventually, he uses his Genie to stop being the Designated Hero and sends the world back In Harm's Way because he finds the happy evilless world exceptionally boring.
The protagonists from Dragon Pink. The only good character is a put-upon Cat GirlSex Slave. In one scene they encounter a group of "Slave Knights", skeleton warriors who defend themselves by keeping a naked girl hostage in their torso as a human shield. The protagonists say "Sorry!" and slash right through one of them, including the hostage. It really says something when the monster is shocked by their callous behavior.
The whole cast really, mainly because this show runs on Comedic Sociopathy. Whether it's the Yandere Shoko or the Brocon Akira, practically every sympathetic character has serious personality flaws to the point where they qualify under this trope.
Vulcan, the main character of Lets Bible, who, within five pages of his introduction, knocks the female lead unconscious and drags her onto his boat with the intent to rape her. When the two of them get attacked, the only reason he protects her is so that he can have his way with her later. Only sheer amounts of Crazy Awesome and Rule of Funny stop him from being completely unlikable (and the fact that he gets better eventually.)
Kaname from Vampire Knight is presented as an antagonistic character throughout the entire story, but it hits full force when he disappears about halfway through without giving a reason and starts murdering and manipulating other vampires who are in turn presented as victims. Towards the ending however, it's suddenly revealed that he didn't really kill his first victim, which somehow, makes him innocent and heroic for having "merely wanted to push people away", and everything else he did is more or less forgotten about - including having murdered the family of one of the other protagonists.
Yuki Cross herself never chooses which one out of two boys (one of which is mentioned above, Kaname and is her brother) to pick, even to the point she has both of they're kids, and tells Zero that she loves him but belongs to her brother.
As noted by Bamboo Dong (on both of her articles on The Stream, and Shelf Life), Akatsuki of Aesthetica of a Rogue Hero is this, to the point where she felt uncomfortable watching it, and on its original stream, dropped it after four episodes. Akatsuki constantly forces women to wear demeaning clothing, disrobes them, humiliates them, like forcing them to wet themselves, and constantly gropes them, all while the show attempts to justify it, and tries to show why he should be rewarded for it. (He means no harm!, Its not rape because shes asleep! etc.)
This is one of the reasons why Chargeman Ken! has become a meme. Ken is always treated as a perfect superhero by the narrative, yet he kills people without caring if they are human or the enemy aliens. Most infamously an innocent professor had a explosive device planted on him by aliens against his will, Ken responded by taking him into his ship and using the poor scientist as a torpedo.
There is also the fact that he began the holy war in the first place and broke the armistice between the demon and Goddess while at it. While his reason was sympathetic, the fallout was so extreme that he is a legitimate target. One of the aforementioned Goddesses themselves said that his sin was so grievous that if the truth came out, no one could forgive him.
An in-universe example from Re:CREATORS (in which fictional characters come to life) would be Aliceteria February. In her homeworld, she is supposed to be a brave and heroic knight, but ends up opposing the other heroic characters and puts innocent people in danger if it means saving her world. After her friend Mamika gets killed, she ends up flying off the rails and attempts to kill Meteora based on circumstantial evidence and even when Sota attempts to appeal to her better nature, she refuses to listen to him and even attempts to kill him if it means getting her hands on Meteora. Fortunately, she later gets her act together.
Kaori Miyazono's actions throughout Your Lie in April are largely built around serving her own dreams and aspirations with little regard for those who stand in her way, or even why they stand in her way. Not only does she force Kousei into returning into the world of music despite his very evident trauma revolving around music (and his unresolved familial issues), she lies to him by never once admitting that she crushed on him, all the way to her death, saddling him with a whole 'nother round of emotional trauma. It's downright amazing Kousei was able to survive the rest of the series with her strangling his neck all the while.
Haruo in Godzilla Monster Planet. He puts his own selfish and self-centered need for avenging his parents after they were indirectly killed by Godzilla ahead of his responsibility for the lives and well-being of the hundreds, if not thousands, of people he is in charge of. Rather than settling on the part of the planet least inhabited by monsters, he chooses to bring the fight to Godzilla and foolishly puts everyone in danger. Dozens of lives are lost before Godzilla Fillius is killed by Haruo, only for the REAL Godzilla to show up and slaughter everyone else with almost no effort.
Hunter × Hunter: Gon can be considered this due to his Blue-and-Orange Morality. He risks his and Killua's lives just so he can meet a father that admitted to abandoning him, and yet he refuses to acknowledge his birth mother because she didn't raise him without knowing anything about her. He sweeps the fact that Killua murdered a handful of innocent people during the Hunter Exam under the rug. He makes Hanzo forfeit his battle by forcing him to make a Sadistic Choice. He threatens to murder an innocent, already-injured girl just so Pitou can heal Kite. When Kite turned out to be fine, he shows no regrets for the lines he crossed just so he could avenge him being All for Nothing.
Shakugan no Shana: The Snake of the Festival and/or Snake Yuji is a rare antagonist example- he is clearly intended to be a Hero Antagonist who has the noble goal of wanting to create a world where Flame Haze, Crimson Denizens, and Humans can life in harmony. But the things he does in pursuit of this goal are rather hard-to-swallow: sacrificing millions of innocent lives, human and denizen alike, in the war, driving Margery to the Despair Event Horizon, and outright kidnapping Shanato become his bride and almost raping her, all while leaving his other love interests Kazumi and Hecate in the dust. Needless to say, some people view him winning and reconciling with Shana as a prime example of an Easily ForgivenKarma Houdini.
Akuyaku Reijo Ni Koi Wo Shite brings us Maria as an in-universe example. The world of the story openly forces her into the "protagonist" role and holds her up as the standard of "heroism" for the entire "The Academy Arc," regardless of what she does. Once that arc has passed, this trope starts being deconstructed as she has completely deluded herself into believing that she, and she alone, is a "real" person, while everyone else is an "NPC" with pre-scripted lines and actions, none of which matter, as long as she follows her "strategy guide." She continues to be shocked and perplexed that the praise and glory she expects... just don't happen.