Radiocarbon dating standard error
A third factor that might make their tests give too young a date, mentioned by Hertz but not by HJ, is the possibility of colonial repairs or "tuck-pointing" to strengthen a pre-existing structure for conversion to a windmill.
In this case, the surface mortar might be colonial, while only the deeper mortar, well inside the joints, would reflect the true date. 93), test cores were taken deep enough to avoid contamination from both rainwater and later repairs.
As originally devised circa 1950, radiocarbon dating was based on the assumption that the proportion of C-14 in the atmosphere has been constant over time, so that the amount of C-14 left in a sample would fall exponentially with its age.
He extensively discusses the recent carbon-14 dating of the mortar by Jan Heinemeier and Hgne Jungner (HJ, 1994).
HJ themselves make no mention that the other samples were taken with a care to avoid repairs.
The primary potential source of bias in the opposite direction, according to HJ, is unburnt limestone particles that may remain in the quicklime after roasting.
I have had a little chemical training (as an undergraduate at Caltech), and some prior familiarity with dendrocalibration, which is an important complication in the HJ paper.
Perhaps they or someone else will be able to correct me, but my reading of their paper is that although the C-14 results are certainly consistent with a 17th century colonial origin for the tower, they by no means conclusively rule out a pre-Columbian origin.