Researchers at Penn State, publishing in the Proceedings Of The National Academy Of Sciences, say, " We prove that, as a consequence of this fact, the time dilation of clocks evolving along nearby world lines is ill-defined.We show that this effect is already present in the weak gravity and slow velocities limit, in which the number of particles is conserved. Moreover, the effect leads to entanglement between nearby clocks, implying that there are fundamental limitations to the measurability of time as recorded by the clocks." In their conclusion the authors state, "These results suggest that, in the accuracy regime where the gravitational effects of the clocks are relevant, time intervals along nearby world lines cannot be measured with arbitrary precision, even in principle."

So basically, if you have been staying up nights hoping for a perfect clock, well, the entrance to the land of high precision horology has a new sign over the gate that says, "Abandon Hope, All Ye Who Enter Here." To read a fairly accessible review of the article in question, check out this coverage from Pionic; if you would like to check out the original paper, it's right here (chock-full of mass-energy equations, but there nonetheless).