Well, if Kurn had been willing to work for a foreign government, he probably could have had an advisory position at the highest level. The idea that he would catch petty thieves on the Promenade was too silly. Rewarding work would be out there for him.
Seriously. Kurn has commanded fleets and they have him frisking cargo ship crewmen.
While I think Kurn and, especially, Worf's, actions in this episode were dumb at every level, in the end, and it might be hard to admit, Kurn was either a coward or a drunk who had given up. He could have (and the people around him could have tried better to help him) found something much more rewarding, like join a mercenary fleet, join the freaking Federation, or in some other way fight for his honor and his place in Sto-Vo-Kor -- like a Klingon. "The true test of a warrior is not without, it is within." Worf tried better with Korris.
Loved the scene where Worf and Kurn infiltrate the Klingon ship though.
Edit: Just put this on, and the scene where Kurn pushes the purple blanket off of him in disgust and starts his "Soft, comfortable..." spiel cracks me up.