Ultimately, the speed of light being the maximum speed limit is written into the fabric of reality itself. But what if were wrong? Is there a way of understanding this result? The simple answer is that we cannot with our current theories and understanding. We would need to overhaul the whole of modern physics, and we would need to find a way of explaining away the thousands of other experiments that over the past century have all confirmed that nothing can go faster than light. We may have to bring back the aether, or modify Einsteins equations. We would have to explain why no other neutrino experiment showed such a result, and why none of the trillions of neutrinos coming from supernovae manage to exceed light speed.
So, yes of course Einstein could be wrong. The whole point of a scientific theory is that it is there to be shot down to be shown to be false by new experimental evidence or to be replaced with a better, more accurate or more profound theory that explains more about the universe. But extraordinary claims require extraordinary evidence, and Einsteins ideas have been checked too carefully for too long for one experiment to come along and destroy all that. But of course that is all it would take if this experiment is proved correct.
Nobel prize winner, Sheldon Glashow, together with Andrew Cohen have predicted that such faster-than-light neutrinos would have to be radiating electrons and their antiparticles, positrons, all along their route from CERN to Grand Sasso via a process called vacuum Cerenkov radiation and hence lose energy. This is not seen. Its a bit like an aircraft that manages to break the sound barrier silently and without a sonic boom. It just isnt possible folks.
So, what would it take for it to be possible. I reckon there are two possibilities (there are other more exotic ones that are rather too speculative):
a) Einstein was wrong and there is an aether: technically, what is known as Lorentz invariance is violated here and there is a preferred frame of reference.
b) Einstein was wrong and Lorentz invariance has to be modified: technically, there may be nonlinear correction terms in the mass-energy relation.
I am not prepared yet to buy into these, or notions of tachyons (hypothetical faster than light particles), or wormholes as shortcuts through space-time or replacing the electroweak theory, etc. All this technical hot air basically means I prefer to appeal for now to Occams razor and go for the simplest explanation: there is still an error in the experiment.