Just wanted to drop my two cents about Bad-Ass!Mihoshi.
IIRC, in OVA3 it is heavily implied that at some point in time Mihoshi actually used to be hyper-competent at her job. Seriously, imagine how scary that must have been for criminals to have someone with Mihoshi's crazy-ass luck as well as a clear and level head that has all the angles covered. It's no small wonder she was once considered the rising star of the GP.
Of course, it's also implied that she wasn't like that all the time. Apparently, from Masishu's perspective, Mihoshi was a fun loving free spirit whenever she wasn't on the clock, and one of the main reasons why Masishu spent so much time hanging out with the Kamiki clan.
And then The Incident occurred - something happened to Mihoshi that very nearly killed her (or maybe even actually did). We get brief glimpses of a limp-faced dead-eyed Mihoshi and... she is not whole.
I'm hoping that we'll learn more about this in OVA4, if and when it ever comes out.