I like to report yet another buggy version of the notorious quest chain called 'blood on the ice":

Recently i finished part 1 of the 'blood on the ice ' quest in windhelm.
additional notes - i did NOT sell the amulet to calixo for 500 gold but used the amulet along with the diaries as evidence against the court wizard 'wuunferth the unliving' as the guilty one so he gets arrested by jorleif.
I noticed the amulet was still in my inventory after finishing this stage, and calixo's shop is permanently closed as well.
A revisit of windhelm some in-game days later there was another murder so i had to talk with the just captured court wizard "wuunferth the Unliving" to begin part 2 of Blood on the ice.
leading to a follow-up quest to patrol the stone quarter area during the night at this point the quest chain starts to be permanently bugged, right after the conversation in jail with the court wizard i notice in the upper left screen the quest update + the new order 'patrol the stone quarter at night" but to my surprise the line "completed: patrol the stone quarter at night' came right after! and i had to 'catch the murderer' as the next order. I walked outside the palace (during day-time) and the floating quest mark pointed me to Calixo running across the steets towards Hjerim where he entered the house. I followed and entered as well where he starts to attack me inside, but he is immortal now and cant be killed even using the console command: "setstage ms11 150' to force finish the quest wont kill Calixo and he even returns to his shop where he locks himself again inside (still remaining unkillable) when you use the command.
The amulet after the console command wont be removed from your inventory either....

i doubt there are other work arounds at this stage besides the console commands, and it is yet to happen bethesda starts to solve quest bugs in their patches.... seems they prefer to distribute patches to patch other patches first.