A few thoughts:
-Make sure your tenant understands that she needs to utilize the police if she feels threatened or feels that she has been assaulted. I'm sure someone who is a lawyer here can provide some better pointers on this end, but you don't ever want to be the primary mediator when something is bigger than the most mundane issues between tenants.
-Figure out a way to not share a backyard when there is a pet involved. I've worked with tenants in 4 different situations where there has been a shared backyard and at least one tenant has a dog. It has never not been an issue. Either someone leaves the gate open, or feels that the dog is encroaching on their free use of the common space, or someone doesn't pick up the poop, the dog is too loud, etc. It may be worth it to just block off access for one unit, or split it awkwardly and have it primarily as a "dog run" or garden type area than a true backyard for either tenant, but definitely do away with the common space as soon as finances allow. It probably wont be all that expensive and will save you numerous headaches.
-See if your male tenant works with any social workers to receive services. This isn't really something you can ask too directly, you don't want to seem like you're setting him up to be discriminated against, but if you're observant, you'll notice pretty quickly if he uses home health services, has a social worker, etc. Many home based services will include a social worker who is probably your best shot at helping him to be a better tenant. If there's a language barrier and hearing barrier, plus the "old and I don't give a damn" barrier, a social worker or family member in the home are usually the only people that can resolve such issues without an excess of emotion. If he is receiving some services, pull them aside or give them a call and inform them about the situation and let them know he could use help in resolving it, as it is "jeopardizing his housing" (magic words). They won't be able to tell you much as they don't have a release for you, but you can tell them as much as you want.
-Worse comes to worse, you can always not renew his lease. I would make an honest effort to avoid that, however, not just because of financial and time costs to you to turnover the unit, but because if he's elderly and hard of hearing, plus on Section 8, he's going to have a rough time finding housing. Obviously, you're not his social worker yourself, nor are you running a charity, but it would definitely be the decent thing to do to make sure you don't end up putting him homeless just because its easy.
Hope you find a good resolution!