I looked at the most awful cases and I think I've figured out what was missing -- a personal productivity / GTD system. From now on, all my candidates must demonstrate their personal system for capturing ALL their tasks and keeping their todo lists synchronized with reality.
Allen's GTD style is not a requirement here. It can be a paper todo list, a Google doc, a mindmap, or whatever else they chose to use. The key here is that they don't forget their tasks, and they get them done without babysitting on my part.
If they don't yet have such system but show promise, I may still hire them, but I'll make it clear that a personal GTD system is a requirement, so if they want to continue working for me, they'll have to develop such a system. And of course I'll be happy to coach them on this.
And there's another key requirement, also related to Allen's GTD. I'm still looking for appropriate wording, but here's a rough draft: The candidates must strive to understand what do I want them to do, i.e. what shape I want to bend reality into using their hands and minds. They must be able to understand and imagine what I want to achieve.