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.
In the Brian Michael Bendis series, he takes on Count Nefaria (a Thor-level supervillain) several times and eventually succeeds in removing him as the kingpin of Los Angeles. He does this largely by enacting schemes that would be insane to try and by listening to the voices in his head (granted, those voices are Captain America, Spider-Man, Wolverine, and Echo). Unfortunately, the real Echo was killed in the attempt.
He also allows Count Nefaria to beat the crap out of him in a police station to give the Avengers time to arrive.
In the Warren Ellis series, his craziness has looped itself so that he's now one man (Marc Spector) and four incarnations of Khonshu, including "Mr. Knight" (a dapper white suit), a traditional crime-fighting outfit, and an anti-magic suit with—in Ellis' own words—a Giant Fucking Bird Skull for a helmet. ("Giant Fucking Bird Skull" has since become a bit of a Moon Knight fan meme.)
Growing the Beard: After he stopped battling Werewolf By Night and became his own character.
Jerkass Woobie: The second Black Spectre, who's so desperate to be unique and special like Moon Knight he becomes a supervillain.
My Real Daddy: Depends on who you ask. The most commonly cited are Brian Michael Bendis and Warren Ellis.
They Changed It, Now It Sucks: Has had this from time to time with different factions of his fandom having less then favorable reactions to certain revamps in his personality and character direction.
The Woobie: Being a superhero with multiple secret identities has driven the poor guy into borderline insanity and he's constantly having to resist Khonshu's attempts to twist him into a Knight TemplarBlood Knight. He's considered C-List Fodder by most of the other superheroes and supervillains and is extremely lonely, to the point of begging to be part of the Avengers once. And then Echo got killed which almost sent him hurtling over the Despair Event Horizon. In short: it sucks to be Moon Knight.