Something has happened to the garden web site, but I will attempt the answer. Getting cold water on the leaves when watering, then exposure to sunlight, can cause spots. Too much sun can cause them. Water with too many chemicals, nematodes, etc. Try watering with warm water near the roots, and don't expose them to direct sunlight, to see if that helps. If not, you may need to sterilize the soil and pots.

"While insufficient sunlight can be harmful, too much sunlight can also cause problems. Among other symptoms, too much sunlight will produce brown spots on the leaves and flowers. This is a form of necrosis analogous to sunburn. In addition, too much sunlight can cause the leaves to curl down and may turn variegated leaves entirely green."

lhttp://www.optimara.com/africanvioletcare1.html

if the spots are lighter, it's usually a sign of cold water on the leaves. African violets are highland TROPICAL plants meaning that they like good moisture, like to dry out in between waterings, and like the water warm. You can get the leaves as wet as you want, just make sure that you dry the leaves without getting the water cold or hot.