Since when is he a hypocrite, terrible detective, or manchild? Or even a psychopath? There are a lot of things wrong with him, but not those particular things IMO. But maybe it’s been too long since I read Watchmen and I’m forgetting something?
He doesn’t try to prevent crime, he simply delights in the sadistic act of beating up criminals, which is ironically a crime.
He instantly judges people based on which side of the law they stand on, but when he is declared a criminal himself, he doesn’t even attempt to reflect on it. He just keeps punching.
When his own friend is revealed to be a rapist, murderer and war criminal(?), he has no interest [“I’m not concerned with speculating on the moral lapses of men who died in their country’s service”], because he doesn’t actually care about crime, he just uses ‘fighting crime’ as an excuse for his real passion, beating up those he considers undesirables.
He’s a hypocrite (and a fascist).
If I remember correctly he was a pretty good detective in the sense that he figured shit out as fast as literal supernatural humans