A few things to bear in mind.
These deviations from the speed of light are one part in 100 thousand. They require measuring the distance travelled to the same precision, i.e. an accuracy of 20 cm!
Relative measurements rather than absolute measurements are usually more reliable. As the Nature News (n.b. not paper) article said
Most troubling for OPERA is a separate analysis of a pulse of neutrinos from a nearby supernova known as 1987a. If the speeds seen by OPERA were achievable by all neutrinos, then the pulse from the supernova would have shown up years earlier than the exploding star's flash of light; instead, they arrived within hours of each other.An earlier anomaly in neutrino physics was of the 17 keV neutrino that was "discovered" in 1985. It is worth reading the historical reviews in Reviews of Modern Physics and Nature which discuss what went wrong. These articles should sober theorists who jump on a bandwagon once some apparent experimental anomaly is observed.
On the other hand, the solar neutrino problem is a case where experimental anomalies did lead to interesting new physics. But note, there the anomalies were by a factor of three in the observed neutrino flux.