Depends on your personal anxiety levels. The situation certainly has never been pleasant, though it’s a lot better in 2012 than it was in 2008, say. At the same time, Naples has never been the country’s hygiene saint. So, noble task forces and political posturing aside there’s no end in sight. The city and region simply can’t keep up with the waste that’s already accumulated and citizens are reluctant to allow incinerators in their back yard. Waste disposal shutdowns backed up garbage starting in 2006, and though some has since been shunted off to Holland, a lot of refuse remains. Moreover, the Campania region (Naples is the capital) has been illegally accepting refuse from elsewhere in Italy for decades (at an underworld profit, of course). It’ll take years to sort out. Meantime, doctors have expressed concern about the increase in the rat, roach, and mosquito presence, particularly in summer.
The other side of the coin is that Naples has been living with variations on this theme for a long time. It’s worsened, yes, but it hasn’t come out of the blue. And (in general) it’s restricted to certain areas of town. Touristy areas have been cleaned out for obvious PR reasons.
So, don’t worry, be happy (unless you’re a die-hard ecologist, in which case stay away). Vibrant Naples is well worth visiting, so is the Amalfi Coast. Put the media hype in context and plan your trip.