Your question rang a bell in my head. I found the following info in an article in the May, 2005 issue of Mississippi Gardener magazine by Stephen Vann.

Your problem sounds like Entomosporium (Leaf Spot of Indian Hawthorn). "The first obvious symptoms usually appear on new growth and on lower branches of a plant. Spots appear first as minute purple dots on the surface of the leaves. The fungus gradually spreads upward within the plant. Under cool humid conditions, spots may rapidly increase in size and number. The spots can "grow" together to form larger areas of dead tissue. Older spots develop a gray center with a raised margin of the individual spots. The centers of the spots contain the spore-producing bodies of the fungus. These structures appear like small black specks about the size of black pepper grains.

Here's what you do:
Collect the fallen leaves and destroy them in late fall or winter. If feasible, remove all spotted leaves already on the plant. Avoid overhead irrigation to minimize leaf wetness. Splashing can spread the spores to other plants nearby. Irrigate with soaker hoses or drip tubes. Avoid summer fertilization that may promote abundant lush growth in the fall. Make sure the plants have adequate spacing to encourage air movement. (At least four feet from center to center.) Several fungicides are available. They must be sprayed regularly and from early season on. Both sides of the leaves must be covered. Look for the following ingredients:
myclobutanil, propiconazole, or triforine.

This disease is also found on flowering quince, pyracantha, some pears, and red tip photinia.

If it comes to it, there are resistant varieties available: "indian princess", "Gulf Green", and "olivia".