I decided to add some trim around the window to cover all the holes and make the window look a bit more finished. I used pine 1x4s to create a sort of simplified Craftsman style casing and installed it with my pneumatic nailer.
Because the trim will mostly be covered by curtains, I simply painted it the same color as the walls.
The trim isn't really visible, but it was worth doing as it required only a small investment of money and time. It's certainly better than two dozen holes scattered all around the window. :)