Could it be thrips? Some of the white spots on the top leaves are suspicious of thrip feeding. And the mention of tiny black spots on the underside may point toward insect droppings. You may need a magnifying glass to see them, but I would look for thrips on the underside of the leaves.
If they do turn out to be the problem, a Google search for thrip control is a good place to find control options. A comprehensive overview is available at http://www.ipm.ucdavis.edu/PMG/PESTNO.... I often try a water spray as a first treatment (not too forceful). Insecticidal soaps or neem oil are popular options.