I wouldn't worry, if I were you: the 'dodgy' areas of Manchester are ones that, as a student, you're hardly likely to end up in.
For what it's worth, I wouldn't flash the laptop in Newton Heath, Ardwick, Gorton or Collyhurst - which are miles from either the University or Halls - and perhaps not in Levenshulme, either, which is quite a bit closer, but still not a place you're likely to end up in by accident.
As far as Moss Side is concerned, it was only ever particularly dodgy ten years ago, and only then if you were black and involved in dealing; it certainly had a lot of gun crime at the time, but it was confined to a very small area and was basically a turf war. The likes of you and me just wouldn't have known it was actually going on. Since then, most of the Gooches - the local gang responsible - have been jailed, a lot of money has been spent regenerating Moss Side, and violent crime has fallen to a level that really shouldn't worry the average, sensible student, who takes average, sensible precautions. The reputation remains only because lazy Southern journalists perpetuate it rather than doing their own research. (If you're of a statistical bent, there are plenty of crime figures available at the GMP website, and at neighbourhood.gov.uk.)