Are there any limits to carbon dating?

Answer 1

Yes:

1. it cannot date things older than ~40,000 years as the carbon-14 isotope has decayed to practically undetectable levels after that much time
2. as levels of the carbon-14 isotope in the atmosphere vary slightly over time (it is produced by the flux of cosmic rays hitting earth, which varies as the solar system orbits the galaxy, etc.) the dating method must be recalibrated using tree ring count reference samples to keep it accurate over long periods of time
3. of course it can only be used to date things that were once living, and thus in equilibrium with atmospheric carbon isotope ratios at the time of death
4. oceanic carbon isotope ratios are different from atmospheric carbon isotope ratios, so this must be accounted for in dating sea creature fossils