Examine your music box to find signs of damage. This could range from obvious defects such as missing parts, incorrect notes and water damage to more subtle issues like color fading or light scratches. Inspect the comb to find broken or bent teeth, a common cause for inaccurate musical playback.
Consider refinishing your music box if you find scratches or discoloration due to sunlight or water damage. Carefully sand away the existing finish with fine-grain sandpaper. Apply a small amount of varnish to an inconspicuous part of the music box, such as the bottom panel, to be sure that it matches any finish that you leave intact.
Listen for squeaks or grinding noises while the music box plays. This is generally due to wear in the dampeners of the comb. Unfortunately, it's simply not possible to just order a new comb and replace the old one, since most combs are totally unique. If teeth are broken off, they can sometimes be replaced at a repair shop. If several teeth are missing, a repair shop can create a new comb from scratch, specific to your music box.
Inspect the cylinder and comb for rust. You can try to remove the rust by disassembling the music box and rubbing it with a bit of steel wool. Be careful, as excessive scrubbing may cause further damage to the components. If you're uncomfortable with the repair, bring it to a shop. You can also practice this technique on a music box you don't particularly care about.
Pay special attention to all of the accessories included with your music box, such as sheet music, the original bill of sale and interchangeable discs. If you're restoring your music box, the potential sale value of the instrument is probably important to you. Keeping all of the minor details in order will greatly increase the value of your music box.