I don't know if this will work for the dirt but if it's just scratches you can get really fine grit paper at an auto parts store (1500 or 1000) and sand very carefully (use a respirator!) then buff and re-poly. actually, sanding would probably take off the dirt too. get as fine a grain paper as you can and work your way to smooth. It's the same principal as taking scratches off one of my dolls. good luck!