Grey Goo: Mostly averted, for the simple reason that the power (and thermal management) requirements are something of a bugger. Breaking a great many of the chemical bonds which make up Stuff requires substantial amounts of energy, which is inconvenient for something the size of a nanite that’s trying to derive enough power from eating stuff to self-replicate as well as consume.
There are nanophage weapons, but they tend to require power from outside (usually in the form of pulsed microwave beams) to work; shut off the power, they stop immediately. Other nanoweapons generally run to the limit of their stored power, and aren’t self-replicating.
Green goos – nanoplagues – are possible, because bio-life tends to contain a lot of energetic molecules, but really, they’re not much worse than regular bio-plagues, except for often having much worse fevers associated with them. And there are plenty of industrial nanopastes that could in theory go golden goo on us, but since the vast majority of those work in sealed reactors or vats and depend on an external power source or feedstock, it’s not a terribly serious problem.
In short, it’s at least theoretically possible that some free-roaming antipollution nanite might cause some trouble one day, but it’s probably not going to be a worse problem than your average “red tide”. Which is by no means to say that it won’t be a problem, but it’s a manageable non-apocalyptic one.