Yeah, I facedesked many times because of this bugged quest.
The problem is, if you do things even slightly out of sequence with how the devs apparently assumed you'd do them, it becomes bugged to hell and unfinishable. My problem was that I didn't wait to sell Calixto the Strange Amulet before I accused Wuunferth of the killings. I had no idea the Strange Amulet was important, and I didn't need the gold; as far as I knew at that point, the Amulet was just a random nothing. It seemed a BIT more important to apprehend the apparent suspect of the murders. But because I didn't sell the Amulet in that first part of the quest, the whole thing bugged out. Now I am stuck with this strange amulet, Wuunferth in jail, and an invincible, eternally hostile Calixto squatting in Hjerim. *facedesk*
Ended up just using the console commands to force-complete the quest, since there was NOTHING else I could do.
Later I learned there was a second part of the quest involving another murder while the Wizard was in jail, I never saw or heard of a second murder until I went and spoke to the Wizard myself, after which a body appeared, oddly enough, and the quest effectively started over. The quest indicated I needed to patrol the stone district at night, I did that and eventually ran into Calixto (who's connection to all this I of course could not be aware) standing motionless next to an argonian female citizen with his blade drawn. Some 10-15 seconds later he kills her and I kill him. I talk to the Steward again and it seems I found "the real killer." None of this made any sense to me as it progressed and now I have a house that's a crime scene and there's nothing I can do about it (apparently). In my experience this quest is quite broken, I don't really know (honestly) how it's supposed to work and like others here I'm stuck with a quest item I can never be rid of. What a disaster indeed.
Tobias, I didn't even get that far. As soon as I got the objective to patrol the gray quarter, as soon as I stepped out the palace door it automatically updated to "find the killer" before I took one step. It was 10 in the morning, and Calixto was nowhere in sight. But somehow my journal thought that I had seen Calixto. I just shrugged and followed the marker to Hjerim. I went in, and Calixto attacks me on sight. I bring him to 0 health, but he doesn't die. He gets back up, just stands there, and I can't kill him or talk to him. End of line. Nothing else I can do...