Yay! Let's all jump on the quantum mechanics physics train!
Another thing wrong with the (in)famous EPR Paradox is that it naturally assumes that, in Einstein's own words, that "God does not play dice with the universe."
To which Niels Bohr replied, "Einstein, don't tell God what to do."
To clarify:
Einstein could not accept that there were some things in the universe that simply could not be accounted for. He disliked that aspect of quantum mechanics (and zero-point energy would drive him into conniption fits, since he won't accept that energy just came out of nowhere) and 'fuzzy math/logic' was not something he was fond of either. Einstein was a proponent of determinism, the philosophical idea that everything happens because an unbroken chain of prior events caused the event to occur as it did due to the laws of causality.
It was his belief that everything in quantum mechanics had a 'hidden' undetermined variable behind it that caused things to turn out as they did. It is this belief, and a rejection of the idea that the universe is a collection of probabilities and/or potentials that allows the EPR Paradox to function as a theory assuming that the two particles are both unaffected throughout their journeys (or that what happens to one happens to the other) and that when the waveform collapse happens once the particle's spin is measured then the information would be transmitted at faster than light speeds to the other particle.
The line of thinking necessary for the EPR Paradox to function essentially blackboxes the universe into a sterile environment and doesn't account for a lot of variables that could effect either particle or the universe they interact with.
That aside, I'm going to play the 'No Cloning Theorem' (put forth by Wootters, Zurek, and Dieks in 1982) as a means to throw something up against EPR.
No Cloning Theorem essentially states that you cannot, in any way, create a copy of an arbitrary unknown quantum state and is the principle under which quantum cryptography functions. This is because to make a copy of anything, you need to know what it is you're copying and by observing the state of an object you collapse the system into a set range of values of the 'observable'.
Consider this explaination, which I shamelessly ripped off Wiki because it's a lot easier on the eyes than what my textbooks tell me:
If Alice wishes to transmit a "0", she measures the spin of her electron in the z direction, collapsing Bob's state to either |z+>B or |z->B. Bob creates many copies of his electron's state, and measures the spin of each copy in the z direction. If Alice transmitted a "0", all his measurements will produce the same result; otherwise, his measurements will be split evenly between +1/2 and -1/2. This would allow Alice and Bob to communicate across space-like separations, potentially violating causality.
It basically states that to even begin measuring the state of his particle (in this case, an electron), Bob would have to produce copies of it which is not feasable since it already violates the No Cloning Theorem and that the copies would all have to give him the same result and in doing so it would violate the hard-and-fast probability of Einstein's thinking and venture into the realm of 'fuzzy logic' (this is roughly tantamount to throwing x number of coins coins up in the air y number of times (wherein both x and y are 'large' numbers so as to satisfy that rule of probability) at once and every single one of them coming to land on their sides each time). This sort of thinking is why any sort of superluminal messaging using the EPR paradox wouldn't function as there would be no way to carry the message in this form unchanged over vast distances unless you blissfully ignore the concept that there
will be change to the particles as they travel.
Like Yangfan said, all you'd be sending out would be noise.
