Dip a piece of aluminum foil in water or a dark cola and rub the brown and yellow spots with it. If the stains are the beginning stages of rust, the aluminum foil will remove it. You can also try a commercial rust-removing product safe for chrome, if desired.
Soak a rag in white vinegar and lay it across the brown and yellow spots for 10 to 15 minutes. Then, wipe the spots away. If they are hard water deposits, the white vinegar will lift them away. Other things you can try to remove hard water deposits are lemon juice or a commercial lime-removing product.
Dab a small dollop of baby oil on a soft rag and clean the chrome with it. Baby oil helps remove stains, and it also polishes and makes chrome shine.