Reliability of carbon dating
Given relatively pristine circumstances, a radiocarbon lab can measure the amount of radiocarbon accurately in a dead organism for as long as 50,000 years ago; after that, there's not enough C14 left to measure. Carbon in the atmosphere fluctuates with the strength of earth's magnetic field and solar activity.You have to know what the atmospheric carbon level (the radiocarbon 'reservoir') was like at the time of an organism's death, in order to be able to calculate how much time has passed since the organism died.
So, if you measure the amount of C14 in a dead organism, you can figure out how long ago it stopped exchanging carbon with its atmosphere.
Reimer and colleagues point out that Int Cal13 is just the latest in calibration sets, and further refinements are to be expected.
For example, in Int Cal09's calibration, they discovered evidence that during the Younger Dryas (12,550-12,900 cal BP), there was a shutdown or at least a steep reduction of the North Atlantic Deep Water formation, which was surely a reflection of climate change; they had to throw out data for that period from the North Atlantic and use a different dataset.
Trees maintain carbon 14 equilibrium in their growth rings—and trees produce a ring for every year they are alive.
Although we don't have any 50,000-year-old trees, we do have overlapping tree ring sets back to 12,594 years.