Wait wait wait... if he isn't paying his share of the rent, who IS?
Also, the idea that the landlord would have to evict you all and that he can't do anything about it is crap. You need to talk to a judge or a lawyer. Something can be done, but it appears as if the limits of your efforts involve posting on ATOT.
Step one is to do as another poster suggested and just take the dog to the animal shelter. Who gives a crap what the roommate thinks. He shouldn't have made it your problem. If you can't do this, you need to put the dog in his room and close the door.
Finally... I don't know what your quality of life is, but if you're living in a house or apartment that has no less than 30 piles of dog shit all over, you and your roommates need to just LEAVE NOW or "physically" tell the guy to get his shit and get out. Whether this means putting his shit out on the front lawn for him to collect or change the locks on him, you gotta do it. Lease or not, you'd be better off having an empty room and paying his portion of the rent, as I assume you are already doing or sticking it out for another two months. If it's THAT bad, maybe you'd just be better off having an eviction on your record.