Carbon-14 is a method used for young (less than 50,000 year old) sedimentary rocks.
This method relies on the uptake of a naturally occurring radioactive isotope of carbon, carbon-14 by all living things.
Natural limitations encompass those as a result of nature.
For example, you may want to date the same zircon crystals using the U-Pb method.
Though, when you come to do this measurement you find that uranium concentrations are very low in your sample (on the order of a few parts per million).
For example, you may want to date a zircon crystal using a secondary ion microprobe (SIMS).
This technique bombards the sample, slowly drawing material out and then sending it through to an ion counter.
This question requires a very extensive answer to be able to cover all bases here but I'm going to attempt to explain the salient facts.
Jump down to summary if you just want to know what both categories of limitations are.