CA,
RE:
Actually because of researching how accurate C14 dating really IS, I went to see why it was denied. It was Answers in Genesis that put forth the assumption that the rate of decay is NOT constant. They give several theories as to why this rate of decay would have changed over time and would now give an inaccurate reading as to the age of fossils and the earth in general.
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In the scientific community, the isotope decay rates themselves are not called into question. The remarkable thing about the process is that the beta decay rate will not tell you when an individual nucleus will decay, but statistically how many are decaying... With Carbon 14 it is a question of the source of the isotopes, engendered by radiative flux in the atmosphere, nitrogen breakdown by cosmic ray bombardment.
But since sequence of events in Genesis 1 and Genesis 2 are not consistent, I would not waste much time worrying about instrumentation issues for measuring occurrence of an event that is described by two differing accounts.
In the first account ( Gen:1) man and woman were created simultaneously after the animals, free to roam the world and were told to be fruitful and multiply. In the second account they are confined to a garden, FORMED from the earth and woman was derived as an after thought when the first man could not find appropriate company among the animals. Even the JW authorities post 1975 admit that they are not sure when Eve was "formed" and hence the uncertainty about the end of 6000 years. Carbon 14 dating will not resolve any of those problems. Uranium half-life dating for the age of the earth might be of some assist though.