Commercial products are available for scratch repair, they are quite expensive. I have successfully removed small scratches using "DURAGLIT" silver wadding polish, this is widely available and not very hard on the wallet.
Always clean the CD from the middle outwards. Don't go around it. A trick to stop jumping, is to get a black permanant marker pen, and very very carefully put black on the outer edge of the disc. I find it easier to balance the disc upright on a firm surface and then gently run the pen round the edge. This has worked for me on several occassions when discs start jumping, though its not a remedy for scratches.
PC World sell a product called Disc doctor which looks like a small fan. It is very good and can repair disc which wont play at all. I think it costs about �30 though cheaper versions could be available
Spellmaster, thank you for your answer. I don't know whether you have a short memory, but you've already pointed out exactly the same thing (CDs/CD,s) on 'phrases & sayings.' YOU'VE MADE YOUR POINT!!!!!