Pests and diseases: Prevention is the best way to avoid pest and disease problems. Start with disease-resistant varieties, keep plants in healthy condition (well fertilized and well watered), maintain good air circulation, keep foliage dry, and remove any diseased foliage or spent flowers. For Japanese beetle grubs, use beneficial nematodes or Milky Spore (Bacillus popilliae). Rose Rx is effective against scale, spidermites and aphids. For more information, see the Pest and Disease Finder.
So grandma had the right idea in the first place, and she really did know what she was doing. It has always been fun to start roses from cuttings. Some people get their kicks by going "rose rustling" in the deserted cemeteries of old and forgotten mining towns. Others just take a twig from their favorite rose and stick it into the ground in their backyard. There is nothing complicated nor scientific about taking cuttings of roses and rooting them to "start" a new plant. There are various ways of taking rose cuttings, so let's tell you how.
Black Spot: Rose plant leaves with black spots that eventually turn yellow have black spot. This is often caused by water splashing on leaves, especially in rainy weather. Leaves may require a protective fungicide coating, which would start in the summer before leaf spots started until first frost. Thoroughly clean up debris in the fall, and prune out all diseased canes.