Pretty much the whole episode "The Courage of Adam", also from the 2003 series. It implies that Adam is useless and really needs his alter ego form to be of any use. It also contradicts many subsequent lessons, about being yourself. Adam is never allowed to develop his own, more realistic character. What we see instead is an instant of little-effort, power-gain transformation.
He-Man and the Masters of the Universe (1983): The first cartoon show had another Broken Aesop, in an episode where a tribe of primitive beings manages to steal He-Man's sword and Man-At-Arms's laser blaster. After the tribe nearly kill themselves by misusing the weapons, the heroes deliver a canned speech on the dangers of weapons. The beings respond by throwing the sword and laser into a lava pit. Of course, our heroes have them back by the start of the next episode... The Aesop apparently being "weapons are bad things, unless the right people have them".
And another one for He-Man. The moral at the end of the episode note "The Return of Granamyr" was that violence solved nothing—this from a guy who wields a great big sword. In that very episode, He-Man dukes it out with a wizard and a demon, and two dragons have at it. The good guys win, of course.
In "Pawns of the Gamemaster" He-Man throws his sword and disarms the titular villain. The episode plays the villain as a cheating coward for not being willing to take He-Man on hand-to-hand. Which is supposed to be a fair fight, despite one of them being a well-trained but mortal man while the other is, as the intro reminds the viewer every time, "The most powerful man in the universe!"
In "The Defection", there the whole thing about people not changing their ways and someone defecting from evil and people don't trust her but she actually does want to change and etcetera and so forth. Except at the beginning of the episode she says that she was once good and was just lured over to the side of evil. So, no, people can't change.
In "Eye of the Beholder", He-Man joins forces with giant insect people and there's the aesop about not judging people by their appearance. Then after a Disney Death, his insect ally returns, having "evolved" into a more human form. So don't judge people by their appearance, because they may actually just be normal looking people who are primitive.
Early in "Disappearing Dragons", Orko's curiosity gets the better of him when he sees the treasure cache of the great dragon Granamyr. He opens a magic bottle and a hand pops out, pulls him in, and beats him up. The episode plot involves dragons being kidnapped to fight against each other for the entertainment of a powerful group of humanoids. At the end of the episode, Orko asks for a reward (or at least some recognition) for his part in saving the dragons. Granamyr's response is to uncap the bottle again, leaving Orko to get pulled in and smacked around again. As Orko gets beat up offscreen (and you hear him saying "OW! Stop! Let me out you big bully!"), He-Man jokes with Granamyr about how handy it would be if he had that bottle, not only condoning the act but basically stating he'd like to open a (literal) can of whoop-ass on Orko. And then the moral He-Man tells us in the very next scene? "There are no dragons in your world, but there are animals, and hurting or teasing an animal is no way to have fun", but apparently the nonhuman comic relief is fair game. Thus handily combining Broken Aesop with Take That, Scrappy!, depending on your feelings towards Orko.
She-Ra: Princess of Power often flipped flopped between "fighting solves nothing" and "you have to fight for what you believe in". Maybe the writers were just trying to cover all their bases. Maybe the titular character was a lady trying to sell action figures (Nah! That's ridiculous!). Or maybe they were saying their fight to free Etheria was futile but worth it. Which would be true, since Etheria was still controlled by the Horde by the end of the show.
She-Ra and the Princesses of Power: Catra's character arc revolves around her belief that she isn't responsible for her actions and her driving everyone away with her cruelty, behaviors which stemmed from her abuse at Shadow Weaver's hands. Catra steadily gets worse until she has no one left and thinks everyone is conspiring against her, creating the message, "You can't push people away and then blame them for your messes". She is called out on it by Double Trouble who shows Catra everyone who has ever hurt her, before saying she's the one at fault. While this was to explain Catra's failures are on her, instead it comes off as blaming her for getting abused.
