During Blood on the Ice, after investigating Hjerim with Viola, she suggested I tell the steward that Wuunferth is the Butcher. Instead of going that route, I talked to Wuunferth and he identified the Necromancer's Amulet and suggested patrolling the Stone Quarter at night. Arivanya routed to the place where the scene in the market is supposed to take place, but Calixto didn't show up. He didn't show up for the next two nights either. I finally discovered that he was stuck in the Windhelm Stables. I had to pick the lock to the stables to get him to come out. Then he headed back into Windhelm and the quest proceeded as it should.
It's possible that this is partially my fault. The quest was left at the stage where you ask Tova for the key to Hjerim for a very long time. It wouldn't completely surprise me given how easy this quest is to mess up that leaving it running for so long contributed to the problem.
This is probably a fluke that nobody else is ever going to be able to reproduce. I suspect even with a game save you won't be able to figure out why it happened, but I do have a couple available if you want to look at them. If so, let me know.
Issue Data
Issue #34294: Calixto stuck in Windhelm Stables during MS11 (Stage 120)