I look first to the artistic styling. The characters and the world they inhabit have to appeal to my eye. Then I look to how those characters manifest their personalities in the situation they are in, whether it be action or comedy.
In action 'toons, I like characters with some inner contrasts -- heroes with flaws, villains with virtues. I also like to see the characters grow over the course of a series run. You don't have adventures week after week without it affecting your outlook somehow. And I want a story where I care about how it comes out. This is all subjective but I know when an action cartoon is a winner for me.
In comedy, I just want laughs. To me, the best comedy arises from how a well-known and well-liked character will react to a new situation. Again, humor is a totally subjective thing, but I know what I find funny and what I don't.
Some pet peeves: Action cartoons where writers pay no attention to the canon of the story's universe, changing its rules without accounting for the change in some fashion. You know, in one episode the hero needs a plane to fly to Europe but in the next episode he travels by teleporter. No explanation to account for the difference. And then there's inconsistent characterization: This week's stoic brooder is next week's life of the party. But no explanation for the change.
There's also the dreaded cardboard character: The hero who's heroic because the writers needed a hero, and a villain who's evil because the story needed a villain for the hero to fight. That often ties in with formulaic stories where you can just about predict what the next scene will be, and usually turn out correct.
In humor cartoons, there are the shows that are just endless strings of lame, tired gags, where interchangeable characters simply spout jokes. And there are the alleged comedy cartoons built around bloody violence and nihilistic destruction as the source of their humor. There's a fine line between slapstick humor, which is funny, and gratuitous violence, which is not. (^_*)
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