Im not sure if "anti-heroe" is the right term.

Its more "morons", i´d say. So, im not looking for series with an asshole, becaise assholes can still be skillful, wise, knowledgable and all that.
Im looking for morons, that arent superskillful, that make wrong decisions, that get called out for that, that behave...like a moron, BUT ultimately have good intents.

So Cowboy Bebop and Hellsing definitely dont fit this explanation, as both Spike and Alucard are far from being morons