I was really sympathetic at first. But even though I'm sure the smell is awful, I'm having trouble staying sympathetic. You refused to try talking and called the health department on them instead, you are eatching their house enough to know that the HD came and gave them pamphlets, you haven't given them a chance to clean them up (maybe they're going to but couldn't right away), and you are upset about their dog that must have been pretty quiet for you to not know was there for an entire week. I sincerely hope you're joking about the signs, but at this point I'm not sure if you are or not.
Instead of sitting there fuming, do the adult thing, go over, take them some banana bread or chocolate chip cookies, and introduce yourself. You would out yourself if you mention the mothballs, but maybe you can get a line of communication going.