Since Jon isn't online right now, I'll attempt to get in a reply ahead of the other upcoming replies.
Carbon 14 dating is but one of the radiometric dating methods. The situation of how and why it works is pretty much unique, relative to that of the other isotopic methods.
C14 dating relates to dating using an atmosphericly created isotope. That is not the case for the other isotopic methods.
Yes, items formed from carbon not derived or not directly derived from the atmosphere can be C14 dated, and you may be able to come up with an age number. That number may well have meaning, but it will not be the date of when the plant (or indirectly the animal) was ingesting atmospheric carbon.
A situation where C14 yields a valid "false date" is where the animal is ingesting "old carbon", which has been long out of contact with the atmosphere. This is how you get such things as 10,000 year dates on living clams.
Sources of truly false dates can occur when the C14 was not produced in the atmosphere. This covers the coal examples.
Other truly false dates can result from contaminations (natural or manmade, in nature or in the lab), poor sample selection (which may include natural contaminations such as zenoliths in igneous rocks), or flat-out blotches in methodology.
Above, I am primarily talking C14 dating. In other isotopic datings, one can also get valid "false dates". You may be getting a valid date for an event, just not the event you think your dating. The prime example of such, is the dating of metamorphic events superimposed on a perexisting rock. The rock may have originally crystalized out at 3 billion years, but a 1.6 billion year metamorphism date may be what you get. Different methods of a rock specimen, using the same or different isotopes, may yield substantially different age determinations. They all may be valid datings of something, the question is what.
Moose
{Edit - Fix typo. Second edit - Tweeked paragraph 4 a bit. Not a content change, but worded better.}
This message has been edited by minnemooseus, 12-28-2005 05:09 PM