Hi Ray,
Range sensitive topic this! I might get string up by the purists here!
But here goes!
Watch case polishing removes a layer of metal to restore the original shine and finish off the watch. It's an art as a bad technique and knowledge can ruin a watch case for good. However a good watchsmith can restore a seemingly battered case and breathe new life into it. (Do a search 'autavia gmt before and after' ).
I would recommend only polishing a watch case if you are starting with somthing battered and junked, with the aim of restoring the entire watch to its factory glory. A polished case but worn out dial and bezel looks....odd at best.
If you have a watch which has taken a few knocks and scratches then I would recommend leave it that way as that adds character to a watch. Purists belive never Polish a watch case, and many wouldn't touch a watch if they suspect its been polished.
In the end is a matter of personal choice, and whether you plan to sell the watch in the future. ..

Hope this helped.

Cheers

: Hello All!

: Please educate me on watch case polishing. Is it ever appropriate?
: When is it appropriate? How does it impact the value of the
: watch? What else does one need to know if considering polishing?

: Thanks,

: RayP