Menses and armpit sweat

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In Cecil’s latest column, at http://www.straightdope.com/columns/021220.html, the master writes:

In 1998, McClintock coauthored another Nature article reporting on experiments in which cotton pads soaked in donors’ armpit sweat were wiped on the upper lips of recipients. She alleged that this process changed the length of the recipients’ cycles, calling the effect “definitive evidence of human pheromones.”

I recall hearing about this experiment on either PBS or the Discovery Channel. Apparently, the people who donated their armpit sweat were all men, and the effect was that women with wildly differing lengths to their menstrual periods ended up with menstrual periods that were all the same length (either 28 days, or “29 days and change”, to quote an earlier Cecil article on menstruation).

The women had little or no contact with each other, and the onset of their menses weren’t synchronized – only the lengths of their menses were affected.

Since the McClintock study had to do with cycle time rather than synchronization, what were the flaws in it that should make us think twice about its results?