call an antique dealer- it does not always work depending on the age

I would advise not having your mirror re-touched. The shadowing of mirrors is actually desirable in the antique community.

You can prevent future darkening and discoloring. Never spray window or glass cleaner directly onto a mirror-- its the matte backing that will start to oxidize and make the shadow spots. Moisten a paper towel with the cleaner, then wipe over the mirror.