Snowdrift mountain laurel
What causes little brown spots on the shrub?
This is likely fungal leaf spots.
Symptoms generally appear in summer but will remain on the plant through winter and can still be appearing in spring.
Leaf blights also cause browning leaf patterns, they differ in that the spots will forms together and the entire leaf will turn brown and drop.
Control is generally with good care and sanitation.
Clean up any dropped leaves and discard of. This helps the spores from spreading.
Good care of the shrub with proper sunlight, air circulation, and fertilizer schedule will help manage these diseases.
Chemical treatment is generally not necessary, but a fungicide can be applied.