Rather than restate every one, scientists decided to keep the inaccurate constant. "Thus," Tim Flannery notes, "every raw radiocarbon date you read today is given as too young by around 3 percent." The problems didn't quite stop there. It was also quickly discovered that carbon-14 samples can be easily contaminated with carbon from other sources—a tiny scrap of vegetable matter, for instance, that has been collected with the sample and not noticed.
For younger samples— those under twenty thousand years or so—slight contamination does not always matter so much, but for older samples it can be a serious problem because so few remaining atoms are being counted. In the first instance, to borrow from Flannery, it is like miscounting by a dollar when counting to a thousand; in the second it is more like miscounting by a dollar when you have only two dollars to count.
Libby's method was also based on the assumption that the amount of carbon-14 in the atmosphere, and the rate at which it has been absorbed by living things, has been consistent throughout history. In fact it hasn't been. We now know that the volume of atmospheric carbon-14 varies depending on how well or not Earth's magnetism is deflecting cosmic rays, and that that can vary significantly over time. This means that some carbon-14 dates are more dubious than others. This is particularly so with dates just around the time that people first came to the Americas, which is one of the reasons the matter is so perennially in dispute.