Are There Things That Can't Be Carbon-Dated?
Yes. The method doesn't work on things which didn't get their carbon from the air. This leaves out aquatic creatures, since their carbon might (for example) come from dissolved carbonate rock.
That causes a dating problem with any animal that eats seafood.
We can't date things that are too old. After about ten half-lives, there's very little C14 left. So, anything more than about 50,000 years old probably can't be dated at all. If you hear of a carbon dating up in the millions of years, you're hearing a confused report.
We can't date oil paints, because their oil is "old" carbon from petroleum.
We can't date fossils, for three reasons. First, they are almost always too old. Second, they rarely contain any of the original carbon. And third, it is common to soak new-found fossils in a preservative, such as shellac. It is also standard to coat fossils during their extraction and transport. Acetone is sometimes used while extracting fossils, because it dissolves dirt. In short, unless you have evidence to the contrary, you should assume that most of the carbon in a fossil is from contamination, and is not originally part of the fossil.
We also can't date things that are too young. The nuclear tests of the 1950's created a lot of C14. Also, humans are now burning large amounts of "fossil fuel". As the name suggests, fossil fuel is old, and no longer contains C14. Both of these man-made changes are a nuisance to carbon dating.
If you hear of a living tree being dated as a thousand years old, that is not necessarily an example of an incorrect dating. Trees only grow on the outside. Wood taken from the innermost ring really is as old as the tree.
http://www.don-lindsay-archive.org/creation/carbon.html
C-14 Decay Profile
The C-14 within an organism is continually decaying into stable carbon isotopes, but since the organism is absorbing more C-14 during its life, the ratio of C-14 to C-12 remains about the same as the ratio in the atmosphere. When the organism dies, the ratio of C-14 within its carcass begins to gradually decrease. The rate of decrease is 1/2 the quantity at death every 5,730 years. That is the half-life of C-14. The animation provides an example of how this logarithmic decay occurs. Click on the "Show Movie" button below to view this animation.
The Limitations of Carbon 14 Dating
Fourth, the ratio of C-14 to C-12 in the atmosphere is not constant. Although it was originally thought that there has always been about the same ratio, radiocarbon samples taken and cross dated using other techniques like dendrochronology have shown that the ratio of C-14 to C-12 has varied significantly during the history of the Earth. This variation is due to changes in the intensity of the cosmic radiation bombardment of the Earth, and changes in the effectiveness of the Van Allen belts and the upper atmosphere to deflect that bombardment. For example, because of the recent depletion of the ozone layer in the stratosphere, we can expect there to be more C-14 in the atmosphere today than there was 20-30 years ago. To compensate for this variation, dates obtained from radiocarbon laboratories are now corrected using standard calibration tables developed in the past 15-20 years. When reading archaeological reports, be sure to check if the carbon-14 dates reported have been calibrated or not.
http://id-archserve.ucsb.edu/Anth3/Cour ... ating.html