I mix up 2 Tablespoons baking soda, a few drops of dish soap, water in a gallon spray bottle and go at it. Spray both sides of leaves and make sure to spray again after it rains. Clears it up in about a week for me.

Watering at night can add to it, if you are spraying down the whole plant. (getting the leaves wet can attribute to disease if they are damp overnight) Is there a way that you can just water at the base of the plants and not get the leaves wet?

 I have used soaker hoses before during the day and they can help a lot, but you have to make sure the hose where the water is coming out is pointed towards the soil and not up towards the leaves. I normally only use the soaker hoses if it is a bad drought or something to give plants and extra boost. I had them under my landscape beds at my old house.

If it is just a few specks, the baking soda spray should help. If it was a ton of leaves, I might suggest trying a fungicide if you can. I had powdery mildew on my crepe myrtles and they gave it to my roses and then to my rose of sharon (all were close to each other in the garden) and I used the baking soda spray faithfully and reapplyed after it rained and it helped tremendously!