Dogs go outdoors to urinate, which protects your floors indoors from pet stains. However, a dog's urine has high salt and nitrogen levels that can damage grass if it raises the nitrogen level in the soil. If you fertilize your lawn regularly, it is possible that the dog urine will add too much nitrogen to the soil and cause the spots to turn brown as the grass dies from high nitrogen levels. This problem may more apparent with large dogs more so than with small dogs because large dogs have larger bladders to empty.
You can train your dog to urinate in one area of the lawn out of the way so it doesn't affect the rest of the yard. This is one way to solve the problem of brown spots all over the lawn. If training the dog to urinate in one spot is not an option, water the urine spots with at least 1 gallon of water as soon as possible after the dog urinates. The water will leach the soil and dilute the nitrogen from the urine.
Dogs will dig to escape or for entertainment if it is bored in the yard. Digging will leave holes in the lawn and a need to replace the soil and plant new grass seed, which is another attraction for the dog to dig.
Dogs left out in the yard for long periods may become bored. If you provide toys for the dog to play with, it will have less time to dig holes. However, you must stay outside with the dog and tell it not to dig while telling it to play with its toys. Once the dog has other distractions, it will learn to stop digging and resort to playing with the toys. In addition, you can take the dog for a long walk every day so it doesn't feel the need to dig a hole under a fence line to get out and explore. Obedience training is very important when teaching a dog not to dig.