There was a case many years ago of a corpse being found in a bog and it was linked to a missing woman, whose husband was accused of her murder. Then carbon dating showed it was an Iron Age bog burial. Peter Garratt got a story out of this which appeared in Interzone; I remember talking to him about it.
But later research showed that there is so much organic matter in a bog that it contaminates carbon dating and the corpse actually was only a few years old.
Doesn't surprise me - carbon dating is only reliable when there is nothing else around to contaminate things. CSI and other TV shows have a lot to answer for, they make these tests look unambiguous, and often there are all sorts of grey areas.
There was an article I remember reading a few years back, think it was in Scientific American, referring to the CSI effect. Jurors in trials are so influenced by these shows that they expect all these tests to be carried out, even when they are irrelevant or would give ambiguous results.
Not really - the radioactive isotopes of silver are only a tiny proportion of natural silver atoms, and their half-life is so short that after that length of time there'd be little or no radioactivity left.
In that case, I think archeologists go through the entire cache looking for the latest coins as that establishes the earliest possible date of the wreck. That can leave a pretty wide field, though, if the last monarch on the coins had a long rule.