Einstein is rolling over in His Grave, or Cern makes a big mistake

I would be quite surprised if this were the answer. The speed of light is known to an extremely high accuracy; the uncertainty is a few parts per billion. In fact, the meter is defined so that the speed of light is exactly 299,792,458 m/s.Given the inherent difficulties in even detecting neutrinos, it seems very unlikely that we would be able to determine the speed of light in a vacuum more accurately by measuring the speed of neutrinos than by measuring the propagation speed of e-m waves which are extremely easy to detect.

For those of us who aren't particle physicists, I think we can put the immediate consequences at something a lot less than insignificant. What kind of thing are you expecting?