For me and my kids, the most important thing isn't the questioning; it's the attitude behind the questioning. I question to learn, and I try to teach my children to question to learn.
I draw a distinction between "doubt" and "uncertainty" specifically because I want my children to embrace the idea that it's ok to be uncertain - but I don't want them to have a "doubting spirit". In other words, I want them to be open to changes in their understanding - of everything - as they learn more, but I don't want their primary orientation to be one of disbelief. I want them to be willing to explore anything and come to believe whatever makes sense to them - but that is different than not being willing to explore some things because their primary orientation is negative and unbelieving.
I'm not sure if that makes sense, but I think the biggest dis-service parents do for their kids in this regard (based on my years of observing parents who preach questioning and "debate" to their kids) is that they do so in a way that encourages their kids to disbelieve - rather than encouraging them to believe.
I try to teach my children to question with the intent of discovering what they can believe (what they can accept as "true" at that time), not with the intent of discovering what they can't believe. It's the focus that matters most - the "direction of the objective", if you will.
Let me use a specific example:
I know someone who was raised to question everything - but it was done in a spirit of debate in which arguing and trying to convince others was the focus. This friend became very good at debating things - seeing both sides of something and making a particular argument well enough to win. He became a lawyer and was very successful - but, in the meantime, he lost his ability to really believe anything in particular. Whichever position could be argued most effectively was the position that was "right" or "true" for him. Hence, he ended up with an orientation geared toward justification, which led to all kinds of destructive beahvior, divorce and other complications in his current life. Right now, he can't shut down his "justification orientation" - and he does whatever he wants to do, since, subconsciously at best or automatically at worst, he can justify whatever he chooses to do in some way. He also can argue about it until anyone who questions him gives up and walks away, further re-inforcing in his own mind that he hasn't done anything wrong.
His problem, as I see it, isn't that he started out with a disbelieving, justifying orientation (although that might be correct); rather, it's that he was tuaght that orientation and it was re-inforced throughout his childhood in the name of objectivity and rationality and open-mindedness. It wasn't a questioning orientation; it was something much more hard to quantify and name - perhaps a "win-at-all-costs" or "pride" or "purely intellectual" orientation.
It's a fine distinction, I know - but it's a very important distinction to me.