Tagging is a huge problem here in Auckland - lots of graffiti everywhere, although having travelled quite a lot in NZ over the past year, I know it's a widespread problem, not just isolated to AKL.
Broken glass is also a problem by the roadside (I cycle daily, so a tad sensitive on the subject), but this is caused by the recycling guys being overzealous when they're loading the truck, or a case of the bottles rolling out of the bins on the kerbside.
Actually, on the subject of tagging - Auckland valiantly tries to paint murals on a lot of public buildings and traffic light control boxes - seems to work and looks great too!