Every so often when I dig up perennials to move or divide them, I notice that some of the finely shredded pine bark that I have used to amend the soil has a white, powdery coating on it. What is it? Is it a problem?

The white powdery coating that you describe is just nature taking its course. The shredded pine bark that you use is just decomposing, and the white is a natural fungus helping the process. This will not cause any problems for you in your garden. In fact, since you have mentioned that you are adding organic matter to your soil and periodically dividing your perennials, that seems to indicate that you have a healthy growing garden.