Thank you for your question.  Your rhododendrons are infected with the azalea lace bug.  The female lays her eggs on the underside of the leaf, and when the insects develop a piercing, sucking appendage, they are able to suck chlorophyll out of the leaf cells.  This results in yellowing (chlorosis).  The black dots are frass (excrement of insect larvae).  These insects were imported, and have no significant enemies--yet!  A parasitic wasp does lay its eggs in the larvae, but the parasitic wasps are not yet in such a great supply that they can control all of the lace bugs.

Here is a link to an Extension article on the bug and some controls.  The challenge of chemical controls is that they have to be applied at the correct life stage of the insect, and needs to 'land' on them on the underside of the leaf.  A challenge!  From an environmental perspective, the other problem is that the chemicals that kill the azalea lace bug also kill beneficial insects, such as bees, pollinating flies, butterflies and moths.  So, I guess we're just going to have to live with them.

I hope this information is helpful to you.  Good luck!

Thanks so much for your quick reply.  When is the best time of year to apply oils or insecticides?

The timing of application is half of the problem.  Are you going to be able to examine the undersides of the leaves to see when they have changed from eggs (which you can neither see nor kill) to nymphs (which can move and eat, but not yet fly)?  That is the critical time, and varies from year to year, depending on the spring temperatures.  That is when insecticidal oils and chemical insecticides have any chance of killing them.  The other half of the problem is that application will require you to lay on the ground (unless you have another clever way to spray up to hit them on the undersides of the leaves) and spray, probably getting the insecticides on you.  If you choose this route, be sure to read any label carefully, and follow all recommendations for safety--as well as not using when there are bees, etc., feeding on the flowers of the rhododendrons.

You can see why this is such a troublesome pest in the area, especially to nurseries that grow them and then can't sell the plants.  Hope this answers your question.