Geoarchaeology:"Artifacts from Akrotiri, linked to the Egyptian calendar [sic] put the Thera eruption at more than a hundred years later [than 1644 +/- 20 BC]. While the controversy remains open, it is our view that the volcanic activity recorded in the Greenland ice core more likely came from nearby Iceland than from the eastern Mediterranean (this may be testable by any chemical signature). [p 158-159]
The Earth-Science Approach to Archaeological Interpretation
by George (Rip) Rapp, Jr. and Christopher L. Hill
reprised from here
"Living samples from a freshwater lake on limestone terrain have been known to give a radiocarbon date of up to 1600 BP." [p 166]
That is one of the poorest things to use for a radiocarbon date. Freshwater shellfish from limestone environments are equally bad.
There are ways to calibrate those kinds of samples but it is easier to use more reliable materials to start with.
There is a large body of literature on this problem.