This shrub looks like red tip photinia. The leaves are exhibiting symptoms of some old cold damage and Entomosporium, a common leaf spot disease. This disease rarely kills the plant, but it is not attractive. In some cases, the disease can be so problematic that homeowners decide to remove the shrub. We do not recommend planting this shrub due to this disease.
The fungus overwinters in infected leaf debris (or on the infected leaves) Practice good sanitation. Rake and dispose of infected foliage, avoid overhead irrigation, and mid summer pruning that may stimulate flushes of susceptible foliage. Registered fungicides may be needed on highly susceptible cultivars.
Fungicides are a preventative and do not control existing conditions. Apply to the newly emerging leaves in the spring and throughout the growing season. Follow label directions. There is not much else you can do. See our website for photos and more information http://extension.umd.edu/hgic/leaf-spot-photinia-entomosporium