I lived in a neighborhood with a halfway house for the mentally ill three houses down the street. (Actually, it wasn't officially a 'halfway house'--the landlord rented rooms to mentally ill clients.) Some were sex offenders, some were violent. Nobody was supervising these people's medications, or making sure they went to their doctors, except for any family members who may have occasionally stopped by. There were about 40 of them living in this house.
I must say that, aside from constantly being asked if I had a cigarette, the occasional panhandler, and the (very) occasional public meltdown (yelling, obscenities, etc.) I never had any problem with any of these people. The police occasionally stopped by, but it was usually to settle disputes between residents, or to haul somebody who'd skipped his meds off to the hospital. I actually made friends with a few of them. I felt sorry for them. They belonged in the hospital; some were quite sick.
Of course, I didn't have children at the time, so I'm not sure how I'd react to living three doors down from a place like this now.
It seems one problem with the word "group home" is that it lumps too many types together --- no one wants a friendly group of women with Downs syndrome to live in the worst neighborhoods --- they don't deserve to live in fear and most are perfectly happy if they can work and earn their own living. They need to live where they can be safe. Same goes for Alzheimers people who are still not ill enough to be in a nursing home --- they aren't generally a problem for any neighborhood. All non-criminals needing group homes should be classifed differently than those living in drug and alcohol half-way houses who have committed crimes, or released from prison sex offenders. A group home for serial rapists is certainly different than one for mildly retarded but completely harmless working people.