Large black spots, usually irregular in shape, on leaves are Black Leafspot disease and are caused by a fungus. The small orange spots are Rose Rust, also caused by a fungus. There are actually several rusts that infest roses. All of them produce the small orange pustules and cause the leaves to yellow and die prematurely. Finally, white spots are caused by powdery mildew, also a fungus microorganism. The late spring rains and the continuing fog and frequent morning fog drizzle are perfect conditions to keep all these diseases going through the summer.
Managing these diseases in roses can be a full-time job. I recently spoke with a gardener who informed me, she spends an hour a day checking her roses. She removes diseased leaves when the first symptoms appear. She also sprays the plants with fungicide as a preventive rather than a cure.
These are good practices if you have the time. My first suggestion is to buy rose bushes with some resistance to disease. There are many, many cultivars and varieties. Check local gardens and make your selections based on the health and vigor of the bush, not just the color of the flowers. There are also several websites which contain extensive information on roses. They often include information on disease resistance.
Most roses will require some spraying for insect and disease control. Triforine, chlorothalonil, copper sprays, Neem oil, and sulfur sprays will help suppress disease. These compounds work best if used as a disease preventive rather than a cure. So check plants frequently and spray at the first appearance of disease. Always read and follow package label direction for best results.