Cracks & Crazing: Dishes often get cracks, some of which go all the way through and some just part way through. Many pieces also get crazing, which are little "spiderweb" cracks that just go through the glaze and not the clay. And those cracks collect dirt, which makes them stand out all the more. What will you do? What will you do?
Hydrogen peroxide. Soak the piece in equal parts of hydrogen peroxide and water. I don't know for how long because I've never used this method before. Once it's done soaking, but it in a bath of pure water for an equal amount of time. This will draw the dirt out of the cracks and make the piece look better, until the next time it fills with dirt, that is. As the cracks dry, a white fuzz will appear. Just wipe that off now and then.
Don't try this technique with bleach as that tends to eat away at the clay. And don't do this to pieces that you intend to sell --it's considered doctoring and buyers will wonder what other defects you're trying to hide. It's always better to err on the side of honesty and present the piece in its natural state.