There seems to be very little random street crime here, which is more than one can say about most major cities. I feel safe on the MTR trains past midnight and do not fear getting mugged or dragged into some back alley to be chopped to bits for my Octopus card and crumpled up 20 dollar notes in my pockets, compared to say Gastown in Vancouver, which is just East of the downtown area by the waterfront.
Major problems around public security here would be:
Triad activity - would be odd if this were carried out in broad daylight, and I'd say that it seldom does.
Domestic abuse/violence - ironically, mostly outside of the public sphere, so it's very much a security issue, just not one that directly impacts the public.