Specimens which lived and died during a period of intense volcanism would appear older than they really are if they were dated using this technique.
Often times, I have come across websites, such as "Answers In Genesis" (Judging from the title, it is obvious that this website isn't really about Science), which shamelessly debunk the basic tenets and empirical methods of Science.
Being the intellectual equivalent of hucksters and mobsters, Creationists of these sort are apt to criticize the Scientific Method in a bid to construe evidence to fit into their biblical bullshit.
So, if we find the remains of a dead creature whose C-12 to C-14 ratio is half of what it's supposed to be (that is, one C-14 atom for every two trillion C-12 atoms instead of one in every trillion) we can assume the creature has been dead for about 5,730 years (since half of the radiocarbon is missing, it takes about 5,730 years for half of it to decay back into nitrogen).
If the ratio is a quarter of what it should be (one in every four trillion) we can assume the creature has been dead for 11,460 year (two half-lives).
C-14 is produced in the upper atmosphere when nitrogen-14 (N-14) is altered through the effects of cosmic radiation bombardment (a proton is displaced by a neutron effectively changing the nitrogen atom into a carbon isotope).
The new isotope is called "radiocarbon" because it is radioactive, though it is not dangerous.
Long regarded with as much vitriol as Darwin's revolutionary idea of Evolution, carbon dating debunks the "Young Earth" Creationist Model: Because of its ability to date fossils upwards to 60,000 years, radiocarbon dating has long been regarded as Darwin's (Read Satan's) advocate.
Discovered by Willard Frank Libby and his colleagues in 1949, during his tenure as a professor at the University of Chicago, Libby invented what would eventually change the face of archaeology by giving a time frame to fossilized specimens.
They thraw through scientific literature, pick the parts that supposedly criticize a scientific method, and put up claims that mainstream Science is bogus.