>For one, quantum electrodynamics, the best theory of light and matter, says photons have amplitudes that allow them to travel slower or faster than c. That breaks the postulates of SR (speed of light is constant, and c is max speed limit).

While perhaps some aspects of the theory will be modified by later theories, I understand that many of the aspects of general relativity have, indeed, be confirmed, for example:

Special relativity: the increase of the mass of particles at great speeds, the "conversion" between mass and energy, the increased lifetime of short-lived particles at great speeds, precise measurements of time (with atomic clocks) in moving aircraft.

General relativity: The advancing of Mercury's perihelion (not predicted, but neatly explained by G.R.), the change of direction of light rays as they pass the Sun.

This doesn't mean that all aspects of the theory are proven, and I think it is precisely because of this that additional observations are made (such as Gravity Probe B).

> ...Last, the major prediction of GR has never been confirmed, the existence of gravitational waves.

That particular point is actually quite easy to explain: the gravitational waves, if they exist at all, are supposed to be very weak. This makes them difficult to detect. Simply making predictions that are difficult to test doesn't necessarily falsify the theory.

>Other peculiarities, such as quantum entanglement and the paradoxic possibility of time travel in GR, further cast doubt on the theory.

Yes, it seems that some of these recent discoveries create certain contradictions.