This is a fungus called black spot. Left untreated, it can cause all the leaves on your roses to turn yellow and fall off. It will also affect nearby plants, as it spreads by spores. Remove ALL INFECTED material and throw it away or burn it. Do NOT leave it on the ground as this fungus is very hardy. It can survive winter and travels very easily, even after being removed from the affected plant. Spray your plants regularly (bi-weekly) in the growing season with a good fungicide (I like the Bayer products). You can also add a little bit of dish soap and baking soda to a spray bottle with water and spray the entire plant.
Please keep in mind that many rose bushes are grafted rose bushes. This means that the bottom part is a hardier rootstock that will withstand cold and heat better than the top and more desired part of the rose bush. Starting a rose bush from cuttings places the new rose bush on its own roots, so it may not be as hardy in cold climates or in extreme heat conditions climates. Being on its own root system can cause the new rose bush to be far less hardy than its mother rose bush.
Despite their reputation for being finicky, most roses are simple to grow and easy to propagate at home. “Propagate" simply means to reproduce a plant easily from a simple cutting. Unlike seeds, which produce very different plants, rooted cuttings produce replicas of their parent. You don't have to be a trained rosarian to reproduce treasured family heirlooms or favorite garden roses.
I planted mine in to the ground just like a normal rose bush, amending the soil with rose fertilizer and alfalfa meal. It is gorgeous, but because it's low to the ground, you should make sure to use drip irrigation or a soaker hose to water it so it doesn’t get black spots from the water splashing on the leaves. If yours is in a pot, let it go dormant in the garage or close to your home to keep the pot from freezing. Keep it watered and in the spring it should come back with more fertilizer to keep it happy.
Northern gardeners need to know exactly what zone a rose is hardy to. Southern gardeners must also watch to see what zones are recommended for each particular variety, as some roses perform very poorly in hot and/or humid weather. Read the catalogs carefully and, if possible, purchase your roses from a local or regional grower. They will be able to advise you from experience about how a particular variety will perform in your area.
Cover the cutting loosely, pot and all, with a plastic bag or plastic wrap and keep the soil moist. Putting a tall stake into the pot will hold the plastic away from the leaves. If the plastic touches the leaves, they remain wet and can succumb to a fungus disease. Along the same lines, make sure the condensation can escape from the plastic or the stem will rot.