Thankfully, I really don't have to worry about any "No Dogs" signs where I live. It is a residential neighborhood, and dogs are only allowed out of a fenced yard when on a leash.
The bad part is that there is no kind of rule that says the dog owners have to clean up after their dogs, and many of the people do take their dogs out and let them run along beside them with no leash. These dogs, of course, just run through people's lawns and do their chores anywhere they please, and the owners just stroll on down the street, and ignore what the dogs are doing.
Many people are at work, so they never even see which dogs are using their yard as a bathroom, and just come home to a dirty yard.
Once a dog starts using a yard, then other dogs also do their chorees there, so it is a continuing problem.
I can understand that dogs need to go somewhere to do their chores; but the dog owners need to be responsible for the dogs, whether there is a "No Dogs" sign or not.
