Thanks for framing my questioning within a larger context. I guess my concept of the power of influence has to do with the evolving role of the educator. Where once we were expected to micro-manage content delivery through traditional methods of teaching, we are now evolving as facilitators of learning.
Part of this process of facilitating is listening to learners and then working with them in the hopes that they can form their own insight(s). I can see some similarities here with mentoring. The danger with mentoring or improper influence occurs when the mentor gets enmeshed with issues of transference and starts "doing" for the mentee/client instead of listening.
I think the major contribution the power of influence can have lies in the idea--be the change you want to see. I have witnessed this idea in action in industry and education and I am always amazed how people respond to models of behaviour and action. It's not an explicit expression of power; it's just a way of being in the world.