Superman at Earth's End has one of these. Superman loses (most of) his powers and has to rely on a gigantic machine gun to solve his problems. After using his gun to kill two Hitlers and a Batman zombie (don't ask) he tells his allies (some little kids with guns) that he's dying. The little kids then bawl and say that guns killed Superman before throwing all of their guns into a bonfire. Of course, no one bothers to point out that guns also saved the kids from two Hitlers and a Batman zombie!
Worse is the fact that Superman himself admitted that the only thing keeping all these kids alive in this After the EndGOTHAM was those guns.
X-Men: despite trying to lecture the world about how great mutants were and how they should be allowed to embrace their identities, Xavier spent most of his life masquerading as a normal human who just happened to be a mutant expert. Xavier only involuntarily 'outed' himself during Grant Morrison's New X-Men run when he was possessed by his evil twin.
James McAvoy said he actually kept this in mind while portraying Xavier in X-Men: First Class. He pointed out that Xavier is a well-meaning, but ultimately misguided liberal, as he still has tons of societal advantages given that he's white, heterosexual, male, and extremely wealthy. He certainly doesn't have to put up with the same bigotry many mutants face (hell, the same bigotry many real world minorities still face), which causes his message of peace to ring false to many.
In general the X-Men books have a theme of how regular humans and mutants should coexist peacefully. The problem with this? Exactly how often did they try to have regular humans around them? How many regular humans were at the institute? How often did the X-Men go to Washington to try to convince legislators to accept mutants? The aesop seems more 'mutants should band together into militant groups to protect themselves', in other words Magneto's message. To make it ever worse, the first comic featuring the X-Men had them casually push around regular human soldiers with their powers because the soldiers didn't want to let them enter a military base.
There's also a dissonance where the fear of mutants is portrayed as prejudice and fear of what's different, but there have been times when mutants - even fully-trained adults - have lost control of their powers without meaning to and caused a lot of damage. In the 80s X-Men cartoon Storm was claustrophobic, causing her to freak out with her powers whenever she was triggered. Mutants are a danger to the normal humans around them no matter how good their intentions are and that is a perfectly valid reason for fear.
Marvel AdventuresSpider-Man # 39 has a foreign exchange student named Kristoff show up at Peter's school, and make a speech about how, unlike many of his countrymen, he doesn't hate America. Peter shows him around, and they talk until it's revealed that Kristoff is from Latveria, home of Doctor Doom. Peter freaks out a bit but accepts him for it. Then the Fantastic Four show up, attacking Kristoff seemingly just because of his Latverian origin, calling him a "potential threat to national security", and taking him away. So, it turns out that he's just a normal, nice kid and the Aesop is that ethnic prejudice is wrong, right? ... well, no, because it turns out that he was Actually a Doombot, and Spidey and the FF have to beat him up. So, the Aesop is that you should never trust people from enemy countries, even when they seem to be perfectly nice, and that it's totally logical to seize and search people who might be a problem.
Marvel's Civil War storyline featured the superheroes favoring registration fighting the superheroes opposing it. Apparently, the two sides were supposed to be presented evenly but due to the clear Aesops of the last century saying that secret identities are good and government oversight of superheroes is evil, it was hard to sympathize with the Pro-Regs. Especially since Iron Man, the Pro-Reg leader, became a borderline Fascist Nazibot for most of the storyline. The whole thing was basically a titanic Idiot Plot where everyone held the Conflict Ball.
The X-Men in particular stayed out of the entire debate surrounding the Super Human Registration Act since in their own comics, government registration of mutants was always portrayed as the first step towards state-sponsored internment/genocide of anyone with an X-gene.
In continuities as old as Marvel and DC's, the inevitable retcons often break initially intact aesops. For example, many of the older X-Men storylines involving Nightcrawler made it anviliciously clear that Fantastic Racism is bad, that we shouldn't judge people by their external appearance, and that having horns and a tail doesn't necessarily make you the Antichrist. Enter Chuck Austen, and it turns out Nightcrawler really was half-demon all along.
One More Day breaks the aesop that Spider-Man is supposed to embody, as instead of taking responsibility for his actions, he dodges it by making a Deal with the Devil against the wishes of its main beneficiary and guilt-tripping his own wife into going along with it. However, in One Moment In Time (popularly known as OMIT), this is retconned so that Mary Jane is the one to have made the deal. Word of God is that the aesop is meant to be "It's heroic to do whatever you can to save a life" but to readers, rewriting history just to save the life of a single person who, in addition to wanting to die anyways and was telling you to let go, let's face it, is likely to die of old age in a few years is simply asinine. The message then becomes "the ends justify the means", and that instead of learning how to cope with loss and move on with your life, you should hold on to what you have and never let go, even if the cost of doing so might be too high; for you and for others.
What makes this even worse is that the "whatever you can to save a life" wasn't selling their souls, give any kind of favor to the demon, or even their love, but he wanted them to give up their marriage. So Peter Parker had to face the consequences of... a chance to get back with Black Cat.
Even worse in that Word of God states that the reason he had the marriage nullified through deal with Mephisto, instead of divorce, is that he felt that having Peter and Mary Jane get divorced would send a bad message to the kids. So... selling your soul to the Devil is a BETTER moral choice than getting a divorce?
The best part of that? Years before One More Day Peter and Mary Jane were ALREADY divorced for some time.
In JLA: Act of God there is an underlying implication that the superheroes were being punished for their arrogance. Even though people like Superman and Wonder Woman are fairly humble in normal continuity (not to mention all the characters who are nothing but humble, such as Captain Marvel), while Batman in this story is ego tripping and denigrating the contributions of his formerly powered friends as they kiss his ass. Apparently the writer thought the superheroes WERE being arrogant because they weren't bowing at Batman's feet and worshiping him as the greatest superhero of them all. This requires the aesop not to apply to Batman, because he's the single most arrogant person in the story.
This is a bit of a mix of Broken Aesop and Family-Unfriendly Aesop, but the moral of Birds of Prey: The Battle Within, the arc from issues 76 to 85, appears to be the fairly stock aesop of "You should accept your friends for who they are and not try to change them," except that what Oracle was trying to change about Huntress is her tendency to kill people. In the end, Oracle apologizes to Huntress, and, in the Dead of Winter story arc (issues 104-108), actually tells Huntress to use deadly force against the Secret Six if she thinks it appropriate, possibly making this the Family-Unfriendly Aesop that sometimes killing people is a good idea.
Mystery in Space #8 featured the story "It's a Woman's World!", in which a man stuggles to prove himself in a future where women have dominated society. It appears to be a story about gender equality, but then you get to the very end, in which the male protagonist forces his wife to do housework, and the wife in turn admits that women ran things long enough and that men should take over again.
The Sandman has a rare in-universe example. The Kipling-quoting "Indian Gentleman" tells his companions a tale he hopes will "prove" that women are inherently evil in "Hob's Leviathan." But the men in the story are no angels themselves, and as his shipmate Hob points out, the sum Aesop of the story seems to be more along the lines of "men and women are both capable of deeply hurting each other."
Uncanny Avengers is the first real attempt at a team book that has the Avengers forming an alliance with the X-Men in the name of promoting diversity and tolerance for the mutant condition — and in some eyes, it's fallen flat on its ass. Issue #5 has Havok give a speech that could be taken to say, "I want to be seen as more than just 'that mutant'"; however, given the wording, many have taken it as saying, "Merely adopting a cultural identifier such as 'mutant' is a divisive gesture that separates us from others." It's not helped by Issue #9, which features such greatest hits as "Members of the majority don't understand why minority puts so much stock in cultural identity" and "Being born with a certain condition isn't a real cultural identity."