Considering how few Japanese dramas get picked up by English-speaking markets, I suppose they can get away with a title like this, but anyway...
If you really enjoy stories about a jaded detective who doesn't get on with their naive idealistic newbie partner, and you don't live in Japan, you may want to consider moving. This is another drama based along those lines, and I really wasn't going to watch it if it weren't for two things. One, the subs seemed to come out quite quickly and that caught my eye. Two, it stars Nagazaku Hiromi who I remember as being the only good thing in the otherwise godawful Cast Me If You Can.
As it turns out, I found that I really enjoyed this. At first it's very generic sensible cop/rebel cop stuff, but about halfway through I decided I really liked the lead character. Hiromi was great in her role as the bad cop: pretty enough that you can see how she charms people when she wants, but old enough that when she acts rudely she doesn't look like a grumpy teenager. Karina, meanwhile, is relegated to the role of the sensible one, and she does okay.
But to be honest, after Perfect Report I'm a little worried about saying how great a series is after only one episode. But, I will say this: About half an hour after I saw Dirty Mama I was wondering what to watch and I seriously considered watching it again. Now that's got to be a good sign.