One of our dogs apparently had a teething problem while we were out working in the garden, and decided to work it out on the wooden door's mullion. The mullion has been rather decreased in the process. I have no problem sanding it back down to shape, then sanding the entire door down and refinishing it; I'd planned to anyway. The problem is that I need to fill these gaps and restore the contours first, and it needs to be more durable than your standard Elmers or Minwax wood filler, which I feel will just flake off.
Painting is probably not an option as we're renting (I'd just use bondo if it was an option) and the landlord was proud of the (horrible) refinishing job she'd done on the door recently.
I've attached two photos to show the damage. They don't show it well -- what you should know is that there's probably at least 1/8" of wood removed in some areas, especially the bottom right of the first image.