If I recall correctly, Einstein was pissed of by the so called "spooky action at a distance", namely non-local interaction. Note however that a many-world interpretation gets rid of that.

Now we have neutrinos that may travel faster than light. That would throw Special Relativity out the window, sure, but not the locality principle: those neutrino do not show infinite speed, unlike quantum entanglement under the Copenhagen interpretation.

He was also upset that it appeared to violate relativity.

To his deathbed he believed in his alternate explanation that the particles were set opposite "at birth" and initiated that way until observation (if I understand that correctly).

So now we have at least TWO phenomena that appear to be "faster than light" - so get cracking scientists (and engineers) on a practical application for communications to probes that are light-hours or light-years away.

I think generally the current theory is that quantum entanglement doesn't allow you to transmit information faster than the speed of light as you can't choose which state your local particle collapses into (although there's some disagreement about whether communication could be achieved with groups of entangled particles) http://en.wikipedia.org/wiki/No-communication_theorem http://en.wikipedia.org/wiki/Faster-than-light (Quantum mechanics section)