Good luck on your interview! Your appointments don't sound excessive, so I really would not worry about that.

I've had interviews where I couldn't come up with an answer to a question, usually because I was a bit flustered or taken aback by what they were asking. If you can't think of a problem you've had at work, maybe you can just tell them that you have been fortunate enough to not have had many problems at work.

With your second problem example, is it possible to phrase it in terms of 'I had a really tight deadline that my boss thought was unreachable, but I buckled down and got the work done-- ahead of time.'

Really, though, I would not worry too much. You never know what they will ask you. Being pleasant and friendly is usually more important than the answer to some canned question.

Good luck on the interview (if you haven't already had it -- I am late coming back to this thread!).