Nitpick: carbon dating is only accurate to about 40,000 ya, so is of little use on the geological time scales you're speaking of. I assume you mean radiometric dating in general, which applies to the use of any or all radioactive isotopes.
https://en.wikipedia.org/wiki/Radiometric_dating
Carbon dating is not valid on geological time scales. However, it has more significance to a Creationist because it is the only one with calculated values that can be 'checked' by non-radioisotope methods. It is also significant because it is the only one which is calibrated using tree rings.
Carbon dating (CD) is the only radiometric method where the radiometric age of the sample can be checked against the historical events witnessed by human beings. Scientist claim that CD is valid for the last few millennia, when we have historic records. The same scientists claim that uranium-thorium-lead dating IS not valid for samples younger than a few thousand years. One can also check the carbon date against tree rings which are counted.
There are a few physical processes that bias the age determined by radiometric dating. Scientists will admit that cross contamination is a big problem which scientists often analyze to figure out the limit the validity. Creationists usually deny that cross contamination is a problem, refusing to check it. Instead, Creationists prefer to argue with the uniformity of physical processes. Many Creationists argue that the rate of radioactive decay has speeded up over the years making the calculated ages of rock appear older. Another gambit used by Creationists is to claim that the initial distribution of isotopes was vastly different a few millennia ago due to the fact that the rock was actually Created.
The initial isotope distribution in CD is determined by the isotope ratios of carbon in the atmosphere. This is greatly affected by the carbon cycle which itself is vulnerable to a lot of environmental variables. For instance, the burning of fossil fuels by human beings has greatly affected the carbon isotope distributions in the last five hundred years. Any plant dated by the carbon cycle in the last 500 years is likely to be biased by the carbon in coal and oil, which is hundreds of millions of years old.
Scientists use tree rings to calibrate the CD age values. Creationists point to this as an example of circular reasoning. However, they ignore the fact that multiple tree rings are used. The calibration is based patterns that occur on a large number of tree rings. They also ignore the fact that the carbon is actually IN the ring. This greatly reduces the amount of error caused by the calibration.
The initial isotope distribution in CD is determined by the thermodynamics of liquids and solids. The working hypothesis is that the rock was created slowly at near equilibrium conditions. If the rock was created in a week, thermal equilibrium is invalid. The isotope ratio would have to be set by God, who created it. Furthermore, the isotope ratio can be changed by rock being heated close to the melting point. The exposure of a rock to very hot water can also change the calculated UTL date by leaching the isotopes out of the rock.
Scientists have shown many UTL dates to be invalid by examining the distribution of isotopes within one crystal. They reanalyze the age using the hypothesis that there were heating events after the rock has formed. They use microscopes on single crystals to figure out what these events are. The events that transpire do not usually correlate with human history records. Creationists will argue that this is circular reasoning.
The big error that Creationists do is ignore studies of cross contamination. Cross contamination is possibly the biggest source of error in dating samples of a relatively low age. Very young samples contaminate the devices. You can't use a mass spectrometer on young samples after very old samples have been examined. The lead in the old samples biases the age determined for the old samples.
Some Creationists will send in young samples to the company, not telling them it is from a recent event. So this sort of ruins it for future customers since the company doesn't know that the old samples are there. You can not use UTL dating to calculate the age of the ash from Mount Saint Helenes, for example, since the ash has an excessive amount of U235 in it.
There are ways to use UTLD for young samples. However, scientific companies usually have a protocol where they avoid dating very young samples. Creationists like to pretend that cross contamination doesn't exist. Scientists and engineers are always studying cross contamination. This is how those limits are determined for radioisotope dating.
