Mildew spots develop on fabric when the fabric gets wet and when it doesn't get a chance to dry out completely. These mildew spores can eventually wear holes in the fabric if you don't remove them. Use a cleaning solution that will kill the mildew spores and remove the spots from the fabric. If the fabric shows visible signs of decay due to the mildew growth, throw it away immediately as it will simply spread mildew to other items in your home.
Bring the fabric outside and place it in direct sunlight for several hours.
Sweep off the mildew spots with a dry brush.
Fill the sink with warm water. Add non-chlorine bleach according to the manufacturer's directions.
Put the fabric in the bleach water and let it sit for 30 minutes. This will kill the mildew spores.
Scrub the spots away with a scrubbing brush.
Launder the fabric as you normally would. Use laundry detergent to kill any spores that might be clinging to the fabric.