Questions like that can themselves be a warning sign, or at least, they have been in my experience. If you're dealing with a HR rep or interviewing for a job that's pretty cut-and-dry, that's one thing. But if your would-be supervisor is asking that sort of question for a job where regular communication with said supervisor will be necessary, then that sort of question is kind of a warning flag. Especially if the whole interview is nothing but those questions.
When I interview, I want to walk away knowing two things; what the employer's expectations will be (and along with that, what the job will really entail), and whether the employer knows significantly more about me as a potential employee after the interview. If all I get are off-the-shelf interview questions, I won't get a sense of either one. What's more, if the questions are coming from my would-be supervisor, then I will get the sense that communication is going to be a regular problem. That's burned me often enough to where I just might walk out...
Yep, as you and others have said, pick a flaw you're willing to "own" and how you overcome it. Everyone has flaws, and good employers want to see at least a couple of things. First, they'll want to know if your flaw is something that can be managed if you look like a good match otherwise, and second, how you yourself react to the flaw.
To give you a personal example (that people are free to rip apart and jump all over), one of my flaws is a tendency to procrastinate. However, recognizing that tendency and being able to spot it when it happens actually helps me to get off my duff and get the job done. I told one person (who later hired me) that laziness is a great motivator; I'd rather get things done so I can be lazy in peace, than be lazy with a dozen things bugging me for attention.