I have many scratched slabs. Is there any good method to polish them in order to remove the scratches?
I've used toothpaste to buff a few of them. It helps if it is just light scratches, but if it is deep scratches not much helps.
Best product for this are the three-step plastic polishes by Novus, sold via Wizard Coin Supply. http://www.wizardcoinsupply.com/plastic-polish/ Goo Gone (used VERY sparingly, it's oily and spreads easily) is good when shooting photos as it tends to fill the hairline scratches that would otherwise catch light and appear in your shots. It also takes off most gunk from stickers and labels people may have attached to the slabs.
Reholdering is $12ea from PCGS and a $10 minimum handling fee for all. I had some sticker residue on the back of a holdered Franklin. I thought I had grabbed some "Goo gone" but discovered it was W-40. For 3 seconds it looked great then completely destroyed the back clouding it over. The coin is ok.
I've sent coins into NGC for reholdering when the slabs were really bad. They charge $10 to reholder, but I discovered that if you send in an already holdered coin for variety attribution, they will reholder it for you for free. Since attribution is $15, it's only $5 more to do this, so if it's worth an extra $5 to you to get a variety on the label I suggest you go that route instead.
And it also makes your slabs smell better BTW, plain ol' Colgate's Toothpaste (the original) works best.
Hmm, I wonder what they would do if you sent in a scratched up multi-slab for reholder. Ya know, because they deny all knowledge of existence and all. Would they split the coins?
I use Meguiar's PlastX, a soft cloth, and elbow grease. PCGS slabs take to being polished better than NGC slabs.