My dog has put some nice 'furrows' in the front and back door from clawing when people come to the door. What's the best way to fill the furrows for painting?

If you fix the furrows this time what is the dog going to do after it's fixed? Get a good grade wood filler or wood repair-Bondo is good-, sand the furrows, fill them, sand in a day or two, prime and paint. I had a dog do that to 3 doors. No longer have dog and nice doors!

Plastic wood also works. It will be a stronger repair, not easier.

I prefer spackling for filling nail holes and small defects in wood which is to be painted. It adheres well, sands easily and most important, does not shrink. Home centers sell a couple brands in small containers as wood filler. One brand goes on pink and dries white. It is labeled as a wood filler but is really only spackling. A small container of spackling is cheaper.