The biggest "problem" with non-nutritive sweeteners is that people think they're all they need to do to lose weight, or even take them an excuse to eat worse in other senses. For that matter, for those used to sweetened drinks but normally drinking diet, it's easy to choose a non-diet one rather than water/tea if there's no diet one to their taste available.

The biggest "catch" (or actual problem, for some of us) with stevia is the funny aftertaste. Although pretty much all non-nutritive sweeteners have some level of aftertaste -- mixing more than one seems to be the least-bad option in diet sodas -- but stevia's is to my taste much stronger. Then again, I really hate the whole licorice/anise/fennel family of flavors, so I'm sure that plays a part.