The important thing is not to stop questioning. Curiosity has its own reason for existing. One cannot help but be in awe when he contemplates the mysteries of eternity, of life, of the marvelous structure of reality. It is enough if one tries merely to comprehend a little of this mystery every day. Never lose a holy curiosity. - Albert Einstein
There are three areas where improved "questioning" can strengthen managerial effectiveness; and it might be worth considering how you can improve your skills in each one.
First is the ability to ask questions about yourself. All of us fall into unproductive habits, sometimes unconsciously. Good managers therefore are always asking themselves and others about what they could do better or differently. Finding the right time and approach for asking these questions in a way that invites constructive and candid responses is critical.
Second is the ability to ask questions about plans and projects. The examples mentioned above both fall into this category. The challenge with questioning projects is to do so in a way that not only advances the work, but that also builds relationships and helps the people involved to learn and develop. This doesn't mean that your questions can't be tough and direct, but the probing needs to be in the spirit of accelerating progress, illuminating unconscious assumptions and solving problems. This is in contrast to some managers who (perhaps out of their own insecurity) ask review questions either to prove that they are the smartest one in the room, or to make someone squirm. On the other hand, many of the best managers I've seen have an uncanny ability to engage in Socratic dialogue that helps people reach their own conclusions about what can be done to improve a plan or project, which of course leads to much more ownership and learning.
Finally, practice asking questions about the organization. Although usually unspoken, managers have an obligation to always look for ways that the organization as a whole can function more effectively. To do this, they need to ask questions about practices, processes, and structures: Why do we do things this way? Is there a better approach? Asking these questions in a way that does not trigger defensiveness and that is seen as constructive is an important skill for managers.
Most of us never think about how to frame our questions. Giving this process some explicit thought however might not only make you a better manager; it might also help others improve their inquiry skills as well.