-Incoherency
There are too many things going on in the story at the same time, and the author's poor transitions doesn't help the fact that it's a monthly release.
-Characters
I hope the posts complimenting the so called character development are joking, because there is little to none. The main character has about as dull a personality as you can get. Also, saying that every character has a unique past is an exaggeration. Everyone one of them have a very slight nuance that distinguishes them from the mold at best. The claymores are almost unrecognizable from each other at times, but that's what happens when you have to create 50+ characters with identical clothing, hair color, skin tone, and figure.
The mangaka also seems to have very little respect for the characters, as many are given unceremonious deaths. I'm all for killing off characters that are past their usage, but when all of your favorite characters are thrown away like trash on a consistent basis, it becomes annoying.
-Art
Starts off poor, but becomes stunning later on. The larger than life monsters remind me very much of Gantz (very different mangas though).
-Story
Starts off mediocre, but becomes brilliant later on, ignoring the incoherency. Nothing like Berserk, for those who mentioned it.
-Slow Start
It's not unbearable, but to say the quality of the early volumes is in the same league as that of later ones is a blatant lie.
Edit: And yes, I have read up to the latest chapter.