Do you think,if those were eggs, they could ever 'pop' with all that white-fuzzy stuff on them?
Because there are so many different types of fungi it is difficult to know how to fight an outbreak. Mold propagates by spreading of spores, which travel through the air, unsterilized potting medium, and water.Mold spores are everywhere, and can grow on almost any organic material, so, mold can considered a sign of organic activity at the root zone. Not all molds are harmful to plants, but they can compete with the plants' roots for air.
You can carefully remove and replace the top inch of soil from the pot, or you could consider repotting. If it is in the dormant stage, allow the soil to become quite dry, then brush off the spores, working outdoors and (if possible) with a fan blowing the spores away. Some varieties of mold are toxic to humans, so please use great care. Wearing rubber gloves and a dust mask are not unreasonable precautions.
How to combat mold?
There are fungicides on the market that will kill the mold, check with your local nursery or garden center for an appropriate one, and use only according to directions. I also would think you could use a diluted solution of bleach or h2o2 on the infected areas to kill it back some in mild cases. To help prevent a repeat occurrence, move the plant to brighter light, make sure not to overwater to much, maintain moderate temperature and humidity, and provide good air circulation. Tilling the top inch of your media on a regular basis a good way to improve aeration and break up compaction.
and about those white pots?..the rule of thumb is not to use any transparent or translucent material..no light to the root zone..etc.