Closers are, for the most part, a volatile breed. They can come out and set the world afire and then crash and burn just as fast. I'm beginning to formulate a theory that I would like to see a pitcher close for 100 innings before he's a safe bet. That is to say.. 100 IP as a team's closer. That's about the point where we saw Turnbow and Dempster fail. Closers not yet there include Putz and Otsuka. Not to say I wouldnt draft guys like that, but I would drop them down my list a bit.
That being said, the position is volatile even if the pitcher is not wholly bad. He could have a bad month or even a bad couple weeks and be replaced, never to get his job back. F Cordero is one who comes to mind, and he only resurrected himself via trade.
Putz is a guy I would put in the 10-15 rank of closers, which means in a redraft I probably would not be picking him.