A mixture of baking soda and water will take care of the mildew on the cover, just wash the inside of the cover with this solution. As for the spots........could be caused from ozone off-gasing, gases given off after shocking (oxidation process produces gases).......Over time the inside of the cover (portion that faces the water) will fade.
Jason,
Store manager for a D-1 & Caldera Spas Dealer