Personally, I don't feel that with three children of your own it's reasonable (or should be accepted) that you basically "adopt" this boy every time you run into him outside. You're not his parent, and by constantly putting yourself/being put in the position of parenting and directing him, it absolves his actual mother of the responsibility she has to supervise her child.
Having said that, I know you can't just stand there and NOT say anything while watching your kids get whacked around and tormented.
You've said that this happens to many children in your neighborhood, not just yours, and that there are no fenced yards or private play areas. I had a few thoughts:
1) Get the other parents together for an in-house play date, and raise the issue of the socially-challenged boy. Discuss what you see the mother doing and not doing in a NON GOSSIPY fashion. Discuss what you see the son doing and not doing. Maybe there are themes to be found; the son might be worse with certain groups and the mother might be better in front of certain parents. Invite the children of the group to as questions and raise concerns. Some may know he's differently-abled, others may not. Having that information may help the situation. If the coffee-klatch turns negative, stop the session and refocus. This isn't about bashing her and her son. It's about putting together a pool of information. This will help you form strategies as a group, and will help you identify situations that invite the behavior/that don't get an appropriate response from the mother.
2) Take that information to the mother. Very, very gently. She may or may not be aware of what she's doing/not doing. She may not care, she may get defensive, she may break down and tell you she's overwhelmed, doesn't have resources, doesn't know what to do. Assert that you and the community are there to protect and raise your own children; it is her job to raise hers. If, after pooling your information, you have suggestions to offer her - do it. If there are ways you can help her, by all means help - if you are comfortable doing so and are able. Suggest resources, offer ideas, and then gracefully back out. You gave her a toolkit, she has to use it.
Don't make caring for HER son into YOUR job. It's her job, and it's appropriate to expect her to care for her child. Her expectation is that you care for your children, right? If your child was aggressive or inappropriate, she would want you to step in, correct? The expectation exists for her as well. If she still doesn't have a clue, can't avail herself of help or resources, or just flat-out doesn't care, then I'd set a really hard line. This isn't about being mean to the harried mommy with the special-needs kid. It's about building a functional neighborhood.
You only have one set of kids. It only takes one time for this boy, either by accident or design, to go too far and harm your children in a way that's irreparable. At the risk of sounding melodramatic, what if he's chasing someone's child with the hand buzzer, and that child falls and breaks an ankle or leg? Runs infront of a car? What if he, intentionally or not, provokes someone's child into smacking him with a tennis racquet? Kids are impulsive. It's not impossible.
As to that hard line, 3) Set up some physical boundaries. You may not have fence, but if the boy is visual, leave some visual cues to designate a physical area he isn't allowed to be in. It doesn't solve the pool issue, but that's up to the lifeguard and the HOA/complex manager. Document each instance, and go to the HOA/manager each time. This is not safe, not at all at ALL, around water. From a liability standpoint, the HOA/manager should be informed. As for your personal backyard, well, Kiddo might just not be allowed past a certain tree or flower bed (things he can't pick up and move), and when he does disregard those directions, your children are to get you and you are to call the offending child's mother and she will, must, and is going to, remove him from the situation. Make the mother aware that this will be your new policy, for the safety of her child and yours.
Sorry for the ramble. Situations like this are so sticky - you have to be compassionate, but it has to apply to your kids AND hers. So difficult to handle gracefully...but my loyalty is always to my own brood. I have to protect my children from the things they can't protect themselves from as much as I am able to.