After I file the scratches or defects out, I cut a small piece of sandpaper (400-600 grit) and wrap it around the end of the same file and sand over the area I filed. You can also attack the areas with Sanding Abrasive Discs. These discs come in different grit and work wonderful. They snap on and off quickly. I would suggest a variety of these as well. The aluminum oxide ones do a great job as well. Also rubber wheels and knife edge Cratex Wheels. You can also get these in different grits.
One thing I am trying to show you is there are different ways to go about getting the same results. you will develop your favorite processes, I am giving you some ideas to go about it, but if you skip the preping process, you work might suffer. Use some or all of these processes to prep your pieces before polishing and you will have a much better polishing experience, and a better looking piece in the end. I will go over some polishing tips soon, so stay tuned.
Now have a Great Day!