The simple answer would be to get rid of the dog. However, I'll assume this isn't a option, but there is not a whole lot else to do. If you can't stand them though, you'll just have dig out those little spots (just rought rake the dead grass and rough the surface up), and spot seed them all. You could put a little topsoil on them, seed them, and then use a product called Penn mulch. Works great for small spots.