It is known that such variations have occurred, but it is thought they can be corrected for by comparing a sample’s C level with the standard curve constructed using samples of known age.
Another assumption is that the amounts of carbon-14 present in the geophysical reservoirs must be constant.
While the small variations in isotope decay that have been reported may not invalidate all isotopic dating, they raise questions about the assumption of completely uniform decay rates.
A second assumption is that the sample being dated has not experienced any loss or contamination of C over its history.
Violations of this assumption can frequently be identified.
Three additional assumptions are necessary in radiocarbon dating in order to estimate the initial concentration of C could be caused by changes in the intensity of the cosmic radiation or in the strength of the earth’s magnetic field.
Carbon-14 dating cannot be applied to materials that have no C dates are less than that figure.
It is sometimes thought possible to extend the dating range a few half-lives, so one occasionally sees dates as old as 70,000 years or more.
The earth’s sediments contain a vast amount of carbon-12 in the form of coal and oil.  Post WM, Peng TH, Emanuel WR, King AW, Dale VH, Deangelis DL. The amount of carbon in fossil fuels is estimated at 6,000 gigatons, and the amount of kerogens (organic) in sediments is about 15 million gigatons.
In practice, there are sufficient variations in these conditions that it is necessary to correct a sample’s raw radiocarbon age by comparing it with the standard calibration curve.
Carbon-14 dating depends on the amount of atmospheric carbon-14 relative to carbon-12.
A final assumption is that the various rates of flow of carbon-14 among the respective geophysical reservoirs must be constant, and the residence time of carbon-14 in the various reservoirs must be short relative to its half-life. (Riverside, CA: La Sierra University Press, 1997), 183. Carbon-14 dating models and experimental implications. Origins 24(2, 1997):50-64  The deep ocean waters are estimated to take about 1000 years to circulate back to the surface: Aitken, MJ.
If these three conditions are met, the initial concentration of C in the sample can be estimated.
The reasonableness of this assumption probably depends on the environment around the sample.