It's true he doesn't seem to have significant failings (aside from poor manners, lol), but Levi is surely more complex than we get to see in the main story. He just doesn't get much focus really. His weakness is probably just not something as visible as other characters' are, and the main story doesn't have time to focus on that. At least that's my guess for now. I just can't imagine them leaving him totally flat as a character.
Actually I wouldn't be surprised if Levi still wanted to kill Erwin, but simply ended up finding the wisdom to restrain himself from getting revenge for the greater good of humankind. He was supposed to be a guy who follows orders from superiors easily (despite being so rude to everybody), yet in the forest he has a strange exchange with Erwin where he's told to refuel (after everyone had thought Annie's titan had bit it) and he seems to question it, before finally following orders. He's a complex guy I think. There's some Eren-like rage in him for sure though. I'd be extremely surprised if those friends of his survive to the end of the story and he's surely going to blame himself for that in part. ((Another guess: Erwin could and should have saved their lives somehow but chose not to, and Levi is entrapped into some kind of bargain that forces him into the Recon Corps. His zeal for killing titans exists because this is his way of getting "revenge" on Erwin, or acting that fantasy out, or something like that.))
