It sounds like what I had and I took a sample to the local nursery. They said it's a disease that begins with "p" and requires heavy pruning back to the live wood. Apparently the branches if crosscut you can see live green flesh and opaque wood. This indicates the limb is dying. There is also a spray to apply to the shrub once you've pruned the diseased parts.

Yellowing of a leaf between dark green veins is called chlorosis and is usually caused by an iron deficiency. Many conditions can be responsible for an iron deficiency. Poor drainage, planting too deeply, heavy soil with poor aeration, insect or fungus damage in the root zone and lack of moisture all induce chlorosis. After these conditions are eliminated as possible causes, soil testing is in order. Chlorosis can be caused by malnutrition caused by alkalinity of the soil, potassium deficiency, calcium deficiency, iron deficiency, magnesium deficiency or too much phosphorus in the soil. Iron is most readily available in acidic soils between pH 4.5-6.0. When the soil pH is above 6.5, iron may be present in adequate amounts, but is in an unusable form, due to an excessive amount of calcium carbonate. This can occur when plants are placed too close to cement foundations or walkways. Soil amendments that acidify the soil, such as iron sulfate or sulfur, are the best long term solution. For a quick but only temporary improvement in the appearance of the foliage, ferrous sulfate can be dissolved in water (1 ounce in 2 gallons of water) and sprinkled on the foliage. Some garden centers sell chelated iron, which provides the same results. Follow the label recommendations for mixing and applying chelated iron. A combination of acidification with sulfur and iron supplements such as chelated iron or iron sulfate will usually treat this problem. Chlorosis caused by magnesium deficiency is initially the same as iron, but progresses to form reddish purple blotches and marginal leaf necrosis (browning of leaf edges). Epsom salts are a good source of supplemental magnesium. Chlorosis can also be caused by nitrogen toxicity (usually caused by nitrate fertilizers) or other conditions that damage the roots such as root rot, severe cutting of the roots, root weevils or root death caused by extreme amounts of fertilizer.

If the soil is too alkaline, acidity may be increased by adding flowers of sulfur (powdered sulfur) or iron sulfate. I add 1 tablespoon of sulfur powder around the base of any plant showing signs of chlorosis. Around established rhododendrons and azaleas, do not disturb the shallow roots. Sprinkle the sulfur under the mulch and then replace the mulch. Do not use aluminum sulfate. Aluminum can build up in the soil to toxic levels eventually. One very common source of chlorosis is when lime leaches out of concrete, such as from a foundation or walkway, making the nearby soil more alkaline. This problem decreases each year as the concrete ages. An annual application of sulfur can compensate for this problem.

If you are on the west coast, you soil can actually be too acidic. If soil is too acid, the symptoms can be the same. Very acidic soil can prevent the roots from taking up nutrients. In the western USA where many rhododendrons are planted in very acidic forest soil, an application of Dolomite and a light topdressing of mushroom manure in late spring is all they need. Sprinkle the lime on in late winter, very early spring. Don't overdo it - just a light sprinkle. If it is mid-spring, get the lime on right away so the rhododendron roots will be able to take up the soil nutrients in time for new growth. If you don't have rain, water it in well.

Here is a temporary tonic for chlorosis:
Purchase a bag of Epsom Salts crystals (magnesium sulfate) (available in bulk at farm-and-feed outlets), and a bottle of FULLY Chelated Iron & Zinc (this is a very concentrated liquid - the chelation means it is in a form that can be readily absorbed by the plant); In a one gallon watering can, put in 2 Tbsp. of Epsom Salts crystals and 2 Tbsp. of Iron and Zinc liquid - fill with warm water and stir to dissolve; Sprinkle this over the rhododendron - by that I mean drench the leaves with the solution and pour the remainder around the drip line of the root ball.