With time, mirrors can show signs of age and wear by developing black spots. The most effective way to correct this is to have them re-silvered, which can be very pricey. If you're just looking for a quick fix, however, this process can help make the dark spots much less noticeable.
Before you can begin, you must determine if you can get to the backside of the mirror without damaging the frame or the mirror itself. Carefully examine the mirror for screws, slats or other hardware that may be attaching the frame to the glass. If you cannot figure out how to separate the mirror from the frame, don't proceed with this process. Otherwise, use a screwdriver or whatever tools seem most appropriate to remove the back or frame and expose the backside of the mirror.
Identify the dark spots by looking through the back of the mirrored glass. You may need to pick the mirror up and hold it against a light source to see them all.
Tear of small bits of aluminum foil and use clear adhesive tape to tape them over the dark spots. Make sure that the shiny side of the foil is against the back of the mirror and that the foil pieces are as flat and smooth as possible.
When all of the black spots have been covered, replace the frame or backing using the necessary tools.