Polishing with "Brasso" or similar metal polish is very effective for
removing scratches from CDs.  It should be similarly effective on vinyl
discs! ;-)

At the professional end of the market, there are real time software
tools made by a UK company called Cedar.  These are used (and abused)
by people who re-master recordings for release on CD.  I am told that
they are both expensive and effective.  I know that lower cost tools
exist; I have no idea of their quality.

One simple trick that can work well is to play the record wet.
Distilled water is probably best for this.  You will be spending
a while cleaning up your turntable afterwards.  This wet playing
technique can also work well with 78s but be aware that some of these
were made with very cheap fillers such as wood dust which swell when
wetted.

Choosing the right size stylus can help too.  A slightly oversize
stylus, as commonly used in the old days of mono gramophones, will ride
higher in the groove and may find a less damaged area.  Conversely,
a rather small stylus will sit nearer the bottom of the groove which
may be full of muck.  Or may be undamaged.

All of these methods (except the first!) have limits to the amount of
improvement they can give.  If the groove shape has been modified by
previous playings then these distortions are virtually irremovable.

I hope that fellow MMDer Robin Cherry will also respond since he has
extensive experience of audio techniques.

Jeffrey Borinsky