It has often been said that there is no such thing as a dumb question. And yet - perhaps due only to inattention, lack of sleep, or hunger - otherwise brilliant people sometimes manage to ask some pretty inane questions during talks. ("Yes, but how does the rover manage to drive around on the moon in the first place - shouldn't it just fall back down to Earth?") Or worse: make false or bizarre assertions. ("I don't see how your thrusters can possibly provide enough lift, given that the moon is made out of cheese!")
Question: How do you answer these kinds of questions in a way that makes everyone feel good about the interaction?
There are sort of three parties to consider here: yourself, the person asking the question, and the rest of the audience. You could, for instance, amuse and satiate the rest of the audience by poking fun at the person ("True, but why would you want to leave a paradise made of cheese?"). Humor might win over the audience, but the person who asked the question will spend the rest of the time ignoring the talk and thinking about how little he likes you. In contrast, you don't want to pander ("Ah, interesting point - I didn't realize the moon was made of cheese. Is it Gruyère or some kind of Stilton?") because, although the person asking the question now feels respected, the rest of the audience thinks you're a schmuck.
Perhaps the question could be re-phrased as:
Question: how do you convince someone they're mistaken without making them feel stupid? (And what if they're stubborn?)
This situation is especially delicate if the question-asker is an established and respected member of your field (since their questions and opinions will automatically carry some weight and authority)---or worse, a person interviewing you for a job! I'm interested in both external tactics (i.e., what do you say?) as well as internal strategies (i.e., how do you put yourself in a mindset where you're unlikely to react with rude or snarky answers in the first place)?