I used those things before, some work well. The one that worked the best for big problems was actually a 'polish' - a very fine abrasive which polished the plastic.
So now I use the best kept secret in CD's to do the same...toothpaste.
Yes, toothpaste.
Colgate is a extra fine abrasive, while Arm & Hammer is a medium grade (don't use it except in extreme desperation!). Polish center to edge, never circular, with a damp super soft cloth. Wash clean and dry. Start very very light pressure, rinse, check, repeat as necessary.
Only Colgate works - Crest is chemically based with no abrasive components (this is beginning to sound like another "tweak" thread!)
Otherwise, best alternate way? Burn a copy - if the drive in the computer can read it better (see if you can write a HD file to buffer the reads) you'll have a perfect copy.