But within the bounds of those assumptions it works very well.
There are the usual cranks who try to work up some tortured logic to attempt to prove creationism, or some variant of a 6000 year old Earth.
The bone has long ago rotted away and has been replaced by rock.
If you've found carbon to date in a fossil, it's a modern contaminant, there's no bone there, it's rock!
The impact of this finding is theoretically revolutionary, and as far as I know, there are no theoretical explanations as to why the decay constant should be dependent on external environmental variables (such as neutrino flux, possibly).
Changes in the Earth's climate can affect the carbon flows between these reservoirs and the atmosphere, leading to changes in the atmosphere's 14C fraction.
So from time to time you hear someone discrediting carbon dating, mentioning that they found a living shellfish that was carbon dated to be 50,000 years old or something like that. Or some idiot says they carbon dated a fossil dinosaur bone to be 5,000 years old or something like that.
Again, DUH, it's a fossil, there's no carbon in it!
Given that carbon dating is not a great deal more than 50 years old as a scientific tool, and it was a considerably blunter and less accurate version back then than now, it seems difficult to understand how an issue so long ago can be meaningful.
It is well understood that as we attempt to date things a very log time ago he accuracy declines, largely because we have to make assumptions about the rate of production of the isotopes that depend on things we know vary but can't directly know what those rates were.
Here's a link: think it's important to distinguish between radioactive dating errors that occur due to -differences in the initial ratio of parent-to-daughter isotopes (due to environmental conditions) in the initial sample (the varying atmospheric concentration of C-14 that make calibration necessary falls under this case), with the actual decay remaining constant -the actual decay rate itself varying (also due to environmental conditions); the possible causal relationship between solar events (neutrino fluxes?