Request for Carbon-14 Dating explanation

Hi, Odessan! I get over there now and again....Welcome to EvC. I'd answer your question, but JonF already did more completely than I could even attempt.

There's another recent study (unfortunately so new that it isn't free on the Science website) that correlates varves in the Cariaco Basin off Venezuela with 14C dates, and compares five other correlations. They all line up very closely back to 30,000 years ago, and then differ by 5% or so back to 44,000 years or so.
Reference is Hughen, et al., Science, vol 303, pp 202-207 (2004).

GIGO at work, it sounds like. What do you think the average lifetime of a carbon dioxide molecule is in our atmosphere?

The reference I gave in post #9 of this thread gives 14C levels back to 50,000 years ago, but I don't think that will help you much. I'm pretty sure in mentions current rate of formation of 14C in the atmosphere: current rate of decay is the same it's always been - half of what you've got every 5730 years.

Rickrose: I'm sure we need a new thread for any real detail on dendrochronology, but in the meantime, you might look at Henri Grissino-Mayer's page:
http://web.utk.edu/~grissino/principles.htm
has definitions and an introduction to how the method works. He has zillions of links elsewhere on his site to the literature, but you may need to be able to read Finnish to make use of all of it.