I always ask the "dumb" questions, even when I already know the answer, because there are always people too intimidated to speak up, and it sometimes facilitates a deeper discussion.
It also gives you cover to ask questions that reveal politically inconvenient truths: you can pretend you had no idea that answer would pop out of it.
(Of course, in an organisation that contains many politically inconvenient truths, you can easily end up doing that too much and people will catch on to it and dislike what you're doing. Another drawback is you have to be willing to look stupid and trust that the stupid first impression goes away with time.)
It took me too long in my career to feel comfortable asking the dumb questions. I would have had a much easier time if I had just asked them. I eventually learned to ask dumb questions when I made a friend who was never afraid to ask then, and it was amazing how quickly he learned.
