Well, Carbon-14 is still the dating technique of choice when dealing with something less than 30,000 or so years old. It only has a half-life of 5200 years, so it's ideal for archaeology, since most things in the human record fall within a few half-lifes of Carbon-14, while something like Uranium-Lead dating won't measure anything that recent at all. So Carbon-14 is perfectly acceptable- when talking about human history. Anything further back than 30,000 years, THEN you get bad research. Any earlier human history - like early members of the genus Homo or late members of the genus Australopithecus - which are highly associated with stone tool assemblages, means you need to bust out the Potassium-Argon or Argon-Argon dating.
Though C-14 is subject to a number of limitations — for one, even touching something can contaminate it, and if it's found in the same context as ash, forget getting an accurate reading. It also gives a fairly wide date margin — four centuries, in fact — which makes it good for a general idea, but absolutely useless for anything more precise. After all, you can learn that the bit of bone you found came from anywhere between 100 CE and 500 CE, which spans completely different cultures or time periods within a culture, so it's not very useful unless you want to make sure it didn't come from somewhere before or after those four hundred years. Being about 500 years or younger is too recent for C-14 dating. Dendrochronology is preferable for anything recent, as well as context; if the piece of bone in question was found in the same context as a style of ceramic made within a 100 year time frame, you're already better off than with C-14 dating. All in all, almost everything you see on TV will be either a research flub or forgetting a more precise form of dating.
This seems natter-like.