I cleaned up mine with a 4" disk grinder. I got the rubber backing plate and screw loc disks. This way I could hold it flat on the anvil. I then worked the face over with a 36 grit disk. When I had most of the tiny dings out I went to a finer grit and worked it some more. I finished with a 120 grit and then gave the entire anvil a scotch brite finish.
If you have big dings or pits I've heard that you can fill these with hard facing rod. I've never tried it however.
I just smoothed the edges a little on mine. The round corners will come in handy as you use it. Even some swayback and big depressions come in handy, as long as you have a flat area for finish work. On mine the front 1/3 was perfect, the back had a slight depression that I left.
Jon