In discussing relativity with a (somewhat mathematical) friend the other day, I ran into a problem showing why special and/or general relativity could be considered as exact descriptions of reality rather than just approximations that are working okay so far. Here's his argument:
Special relativity applies to a situation where there is no curvature of spacetime. Since both matter and energy cause curvature, the only situation where special relativity would apply would be one which has no matter and energy, and therefore one which is not achievable in any experiment. And even as a thought experiment, a clock has to have mass and energy and so there can be no exact predictions in such a theory.
He went on to say that therefore the general theory of relativity rests on a very shaky foundation. This is as compared, for example, to thermodynamics which rests comfortably on statistical mechanics and quantum mechanics.
A related question: Special Relativistic approximation to GR