I'm having an issue with the second part of Blood on the Ice. My objective says Catch the Murderer, and every time I go into my house, Calixto is there. I can't kill him or talk to him.
I'm on PS3 and I've bought the house, have the amulet, etc.
Any help would be appreciated.

thats odd...he shouldn't be in your house, you should have found him when you were "patrolling the stone district" However, that was absurdly easy because if you try to talk to him it says "this player is busy" so I knew right away that it was him...I guess reload, cause if you can't talk to him you can't do anything to get him to leave...

I had this issue. He was in my house and would continuously attack. I'd knock him down, and he'd get back up again and attack me. The only way around it was to use the PC console to move past that part of the quest. Even after I finished the quest, he was still alive - and summoned a guard to attack me for breaking into his house. Still couldn't kill him.

I also had to use the console to remove the 'Strange Amulet' and add the correct amulet. It never gave me the dialogue option to appraise / sell it to him.

This quest was just a pile of bugs all around.

I don't know of a fix for this, but I know the cause -- if the objective to "patrol the Stone Quarter" completes almost as soon as it's received, then Calixto's final victim is already dead. The game randomly selects one female NPC in the "TownWindhelm" faction to be the victim.

Now, what if no woman in Windhelm has been killed, either by you or a dragon? There is a rather large problem with the parameters of selection. In the ruins of Alftand, there is a dead Altmer woman who happens to be, by some accident, a member of the "TownWindhelm" faction. If she is selected as Calixto's victim, the quest cannot be completed. Worse, reloading will not help -- the final victim is selected when the quest starts (or, in other words, when the scene in the graveyard occurs). Of course, this can also occur if Calixto's victim does by any means beforehand.

Patch 1.3 claimed to fix issues with Radiant Story selections, and since then, I've done the quest twice with no trouble. But two out of three isn't conclusive, so I'm not certain if this is fixed at all as of late.

The safest method to complete this quest is to side with Wuunferth, as Calixto's victim in this case is always the same woman.

To see who was selected as the final victim, PC users can use "sqv MS11" in the console, and scroll up until they see the alias "PotentialThirdVictim"; using "prid [whatever the number was]" will select the victim in the console. From there, "moveto player" or "player.moveto [the number]" will bring the victim to you or you to the victim.

Otherwise, if all else fails, use the console to update the quest and use "disable" on Calixto.