What is the most difficult problem
you faced in web designing (javascript or css related) and how
did you debug and solved it?
You see the point I'm making? Not that asking this question is wrong. I would ask it for perspective and to get me thinking about my experience. ("Oh, yeah. I did something like that once.") However, it seems that you want to substitute the experience of someone else for your own. Unless the interviewer doesn't know what they're doing, they'll see through it.
Edit: Specifically, I would only ask people to tell me the types of problems they've solved.
Edit2: Then, I'd try to recreate and solve them on my own, if possible.
Edit3: The only thing that comes to mind ATM, is wrapping my head around just what 'this' means in JavaScript.
I also ran into a hairy issue using jQuery to create a tabbed interface. The close tab icon (an 'X' icon) kept moving around, seemingly at random. This was also a lot JavaScript event hell. (The situation where the meaning of 'this' is very important for the structure of the code.)