mr. clean
THE HARDCORE JANITOR
They say cleanliness is next to godliness. If that's true, this guy is in pretty good shape.
Which is to say, Levi has a bit of a problem, and that problem is he is a clean freak. Big time. In fact, it's one of the first things we learn about him when he is introduced in his special chapter. Not long after that, we get to see how it manifests itself: after dispatching a titan or two, Levi notices he has blood on his hand and blade and immediately stops to wipe it off with a handkerchief. Gross.
Levi's penchant for cleanliness is one of the ways his character is "played down" a bit from being mankind's strongest soldier. Clearly, he's far from perfect, despite the hefty title. His neurosis is often depicted in a somewhat less-than-serious manner, which I found refreshing in such a serious story.
As it progresses, you see several more instances of his preoccupation with cleanliness. When the Special Operations Squad (lead by Levi and formed to keep an eye on Eren) arrives at the old Survey Corps headquarters, Levi wastes no time giving his first order: the place is filthy and he won't be having any of that, and immediately divides up responsibility for whipping it back into shape. However, his standards for cleanliness are very high, so he sometimes finds other people's cleaning skills lacking. Later, his plans to continue the cleaning blitz are thwarted by Hanji, who has other ideas. This disappoints him, of course. That yard is probably totally gross.
As a side note, Levi doesn't have any qualms with telling us how he really feels about gross things. Eren's regenerative ability? That's just nasty, man. It's probably safe to assume that Levi is a bit of a germaphobe as well. It's more subtle, but you can infer it from the way he tends to hold his cups, with his hand covering the top. I guess you can't really blame him; you never know when something might explode and send shit flying everywhere. Who wants that in their coffee?
While it's usually played up in a lighter way, there are instances in which Levi is shown to be affected by his cleanliness issues even in very serious moments. He still takes the earliest safe opportunity to wipe blood from his face, and he even comments about how dirty Eren is after busting him out of the mouth of the female titan. You know, while fleeing for his life.
Levi remains a sparkling diamond in a world of blood, sweat, tears, and all that other gross stuff.