i really havent felt unsafe in manchester, and i have been to quite a few areas with bad press (completely unintentionally, i get lost a lot). there have been a couple of incidents involving students, but i havent had anything happen to me. obviously if you are a knob and go looking for trouble, you will get it, and if you are not cautious with regards for your personal saftey you might be in danger. obviously some people take all the care they can and still get attacked or something, but this is rare and happens anywhere, not just manchester. and there isnt a really huge police presence or whatever but they are around, you do see them occasionally, i remember on a friday night in fallowfield there were a couple of mounted police hanging around the sainsbury's car park, the horses scared the crap out of me but it's nice to know they are there if something did happen.
like babyshambles, i feel more comfortable walking around manchester than i do at home, but then i do live in one of the roughest south london suburbs that is swarming with chavs.
but yes, didsbury is a very pleasant place.