If you want to clean an antique mirror, you should take into consideration both the frame and the actual mirror. The product you use to clean the mirror should probably not come in contact with the frame, particularly if the frame is antique as well. It would also likely be safer to clean your antique mirror with homemade cleaning products instead of commercial products, which often contain a variety of chemicals that could be damaging to your mirror. You should additionally try to avoid using a spray bottle on your mirror if it is attached to an old frame and instead use a lint-free cloth saturated in your cleaning solution to wipe the mirror clean.
Antique mirrors are usually much more delicate than other types of mirrors and are often silver-backed, which means it may be best to use a delicate cleaner rather than a harsh commercial cleaner. To make your own delicate cleaner to clean your antique mirror, you can mix up two parts of water to one part of rubbing alcohol. If you don't have rubbing alcohol, you can use two parts of water to one part of vinegar instead. If your mirror doesn't have an old frame attached, you can pour the solution into a spray bottle and clean the mirror with it in the same manner as you would any other mirror. In the event that an old frame is attached, you probably don't want to get your cleaning solution on the frame, so you should instead pour your cleaning solution onto a lint-free rag and wipe the mirror clean with the rag, adding more cleaning solution as needed.
If you have gotten some of your cleaning solution onto the antique mirror frame, you should use a dry cloth and dry off all the moisture you find on the frame. Moisture that is allowed to sit on antique wooden frames can severely damage them, so it is very important that you make sure all moisture is wiped away. If you want to clean your antique mirror frame, you should try to use water and avoid any other type of cleaner because you can't be sure what the results of using anything else might be. After wiping down the frame with a wet rag, thoroughly dry it off with a dry rag.
Once your antique mirror is clean, it should be easier for you to spot any damage. Silver backing on antique mirrors tends to chip away over time, and spots that have chipped will be more noticeable if you shine a light directly into the clean mirror to inspect it for damage. There are antique restoration specialists who can re-silver antique mirror backing as well as repair other types of damage to antique mirrors. You may not want to attempt to repair your antique mirror on your own unless you have some experience in furniture and mirror restoration.