Carbon dating has a certain margin of error, usually depending on the age and material of the sample used.
Carbon-14 has a half-life of about 5730 years, and therefore it is used to date biological samples up to about 60,000 years in the past.
Beyond that timespan, the amount of the original C formed by irradiation of nitrogen by neutrons from the spontaneous fission of uranium, present in trace quantities almost everywhere.
For these samples, other dating methods must be used.
Furthermore, if a sample has been contaminated, scientists will know about it.
Ironically, given how supposedly useless carbon dating is claimed to be, Creation Ministries International rests part of their "101 Evidences" on carbon dating being a useful method for within several thousand years.
The level of atmospheric C is not constant due to human activity, in part because of human combustion of fossil fuels and in part because of above-ground testing of the largely defensive weapon of the thermonuclear bomb.
However, calibration of carbon levels using tree rings and other sources keep these effects to an extremely small level.This is meaningless because dinosaur fossils are not dated using carbon dating; dinosaurs became extinct 66 million years ago, more than a thousand times farther back than carbon dating can be used.This of course contradicts claims that the Great Flood messed up how carbon was deposited, destroying their own argument.Less astute creationists often conflate carbon dating with other forms of radiometric dating, attempting to "disprove" the true age of dinosaur fossils by "refuting" carbon dating.
Carbon dating, like other radiometric dating methods, requires certain assumptions that cannot be scientifically proved.These include the starting conditions, the constancy of the rate of decay, and that no material has left or entered the sample.