Dog Urine has a high level of Nitrogen Salt which in small doses can fertilize patches resulting in Green Spots. Many times the salts are so strong that they actually kill the grass in that spot.
What can you do about Dog Damage?
There are a few basic approaches to fixing dog damage:
Apply something to the grass area after the dog pees to help the salt move down through the soil. This can be difficult to do, but if you make a practice of watering pretty regularly in the dog pee area it might help.