First, the Ehrenfest paradox has been resolved adequately when GR is involved, as explained in the Wikipedia article, so it is unlikely to be relevant here.

Second, every physicist knows that SR is incomplete (it leads to GR, which doesn't play well with QM), so a more accurate theory has to come along eventually. That said, not many people expected that a straightforward low-energy measurement like the OPERA one might be enough to show the limits of local Lorentz invariance. Of course, it in no way invalidates relativity, whether you like it or not, just outlines its potential limits.