I completed the Hired Muscle quest in Riften from Farkas. Vikas gives me the Rescue Mission quest to save a woman from Markarth who has been captured in Morvunskar. I've already done the Sanguine quest and after that went back to Morvunskar randomly and killed the jailor (I'm betting this is where my problem comes from). Anyways, a few minutes after this quest is assigned to me it appears in the 'completed' column but for all other purposes it looks like I haven't done it. The companions won't give me new quests (tell me I already have one). When I go to Morvunskar, the woman I'm supposed to rescue isn't there. Instead, she's still at the inn in Markarth. I can't get the quest to start properly and thus I can't do the purity quests for the companions. Got me to stop playing the game.
The only other bugs I've encountered are
1, The skald bounty bug not clearing (seems pretty common)
2, If I got any sort of bounty in Markarth or the Reach, even if I paid it off or the witnesses were killed (I got one when some Thalmor attacked me when they didn't like how I was talking), the Thalmor in the keep will attack me, causing everyone else to attack me. I ended up killing the Thalmor and that settled everyone down to where they act normally though I fear that will come back to haunt me on a dark brotherhood quest since I know that Thalmor character shows up again to play a minor role at a dinner party.