The Assassin's blade quest appears to be bugged at several points. I've gathered from other forum posts that the blade should be unequipped for the quest to work properly.

Whenever you want to abandon the quest / not kill a man with doggies, you get a message saying the blade crumbles. If you have the blade equipped, it doesn't crumble.

And in the end when you are in the "have the blade" part of the quest and return to initial location, the quest doesn't end if you have the blade equipped. I actually got a new quest from the same location and was quite confused before doing some searching on the forums.

In short: Assassin's blade quest all borked up if you equip the blade like the quest description implies (kill folks with blade implies equipping it, I think).