Dating artifacts (Young earth vs old earth)

Here's one that gets thrown around a lot, courtesy of RAZD:

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By counting varve layers of diatoms in Lake Suigetsu in Japan, scientists lead by Dr. H. Kitagawa were able to establish a chronology extending the calibration of radiocarbon dating to 45,000 years ago as well as confirming the tree ring data (note - the carbon 14 abbreviation used in article changed to "C-14" here for consistency):

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Lake Suigetsu is located near the coast of the Sea of Japan. A 75-m long continuous core was taken from the center of the lake. The sediments are characterized by dark-coloured clay with white layers due to spring season diatom growth. The seasonal changes in the depositions are preserved in the clay as thin, sub-millimeter scale laminations or "varves". Based on observation of varve thickness change, we expect that the annually laminated sediment records the palaeoenvironmental changes during the past 100 ka.

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This sequence of annually laminated sediments not only forms a unique continuous palaeoenvironmental record after the last interglacial but also permits us to reconstruct a complete C-14 calibration extending back to at least 45 ka BP, and probably even more by means of combined isotope enrichment and AMS C-14. We have performed AMS C-14 measurements on more than 250 terrestrial macrofossil samples of the annual laminated sediments from lake Suigetsu.

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Here's a graph corellating the radiocarbon dates of the material of the varve layers with their annual position in the layers:As you can see, the correllation is quite profound. The dating is slightly off; this is due to cimatological effects on how carbon has been accumulated in living things. Also, you'll see a few outliers representing procedural error in the laboratory.But the vast, vast majority of dates, as you can see, correllate very well. Radiocarbon dating is a valid dating method.