Ah yes, the good old creationist argument: "If something is wrong, then maybe everything's wrong." Imagine if I had the following conversation with my dad:
Me: What did Mum cook for dinner yesterday?
Dad: Hmm, I think it was pasta.
Me: Do you know for sure that Mum is loyal to you?
Dad: Of course!
Me: Actually, Dad, I checked the fridge. Yesterday we had rice for din -
Dad: EGADS! Everything I knew about Mum might be wrong! She must be cheating on me!
Science proceeds not just by demolishing old theories but by building new ones. Not only that, new theories must accommodate the observations that old theories once explained. You talked about drivers not needing to know physics to drive their cars - true, but
someone's got to know enough physics to actually
make one, doesn't he? And if scientists create an extension to the Theory of Relativity tomorrow which predicts that my car should never start unless I replace all the petrol in the tank with soapy water, I can immediately tell them they're wrong, and so can you.
See? Any theory replacing the theory of relativity will have to accommodate all the phenomena the theory of relativity once explained, including why we have been accelerating plenty of other particles to within an inch of the speed of light for decades now without ever seeing even one of them cross the light speed barrier.
Like I said, you won't be moving around superluminally any time soon until we turn
you into neutrinos. And why exactly do you think the human race will be visiting stars? Don't you take conservative eschatology seriously?
In any case, some theoretical physicists have been beating the stuffing out of the result. Andrew Cohen and Sheldon Glashow (yes, the discoverer of the electroweak) have calculated that neutrinos really traveling that fast should have spit out tons of energy in the form of electron-positron pair emissions, disallowing them from reaching OPERA with the claimed energies; and yet another theoretical physicist blogger has given quite detailed possibilities for unnoticed errors, including a list of errors which aren't big enough to explain the result (most of them GR-related). See links here:
Superluminal Neutrinos Would Wimp Out En Route | Degrees of Freedom, Scientific American Blog Network
The Reference Frame: Potential mistakes in the Opera research