The particular field that I know best where Kuhn's critique applies is that of psychology. For many decades, Skinnerian behavioral psychology was the orthodoxy for the scientific approach to psychology. Back in the day, if a scientist wanted to pursue a more cognitive approach, he would be squeezed out of the field. The rationale for this from the behaviorists was that cognitivism was anti-scientific because it posited complex internal mental states that could not be directly observed, which was considered to be counter to Empiricism, and hence anti-scientific. Behavioral psychology was based on the premise that mental states are very simple, and therefore that nearly everything important can be easily measured by directly observing behavior.
In their enthusiasm to be "scientific" and promote objective measurement, the behaviorists missed something very important: That their model was completely wrong. Wanting something to be easy to measure doesn't make it so. And the cognitivist claim that people have complex internal states is not anti-scientific, despite the protests of the behaviorists.
The "paradigm shift" did eventually come, when no other than Noam Chomsky published a devastating criticism of behaviorism that opened the door for the cognitive approach to be taken seriously. But this didn't happen without a fight that had lasted decades, where many careers were needlessly ruined, and the entire field was held back by decades.
The fact that Kuhn was so right on is seen by the fact that Kuhn's book was actually written before the Behavoirsim -> Cognitive Psychology shakeup was complete. The most prominent example in Kuhn's book, I believe, is for the rise of quantum mechanics.
Where is the problem? There is an implicit, and idealistic, assumption here that science is flawed because the implementation scientists have is less than perfect and new ideas are not accepted instantly - despite there being very good reasons for this, and, in the long run, all of this working perfectly well to advance human knowledge.
Also, what was not so apparent pre-Kuhn is that proponents of the new paradigm were often forced out of the field altogether if the time was not yet right.
To conclude that this means that science is "flawed" is a value judgement. But it certainly means that it is not an idealized puck on a frictionless plain.
I hope they are reading the prior literature on the science of evolution, for example as assembled in the "29+ Evidences for Macroevolution: The Scientific Case for Common Descent,"
http://www.talkorigins.org/faqs/comdesc/
so that they understand what "Darwinism" is today after 150 years of scientists checking facts and refining the understanding of the origin of species. Alas, there are still spectacular examples of people who purport to be scientists who disagree with Darwin
http://scienceblogs.com/pharyngula/2012/07/21/creationist-fu...
who totally misunderstand what Darwin meant and what evidence has turned up in more recent generations to refine our understanding of evolution.
https://www.google.com/search?q=29%2B+Evidences+for+Macroevo...
e.g., A Critique of Douglas Theobald’s “29 Evidences For Macroevolution” http://www.trueorigin.org/theobald1a.asp
[1] http://darwin-online.org.uk/contents.html
[2] Finding a species that won't fit in any taxonomy, a dog giving birth to a non-dog, finding a fossil in the wrong layer, etc.
(No, real scientists don't call it Einsteinism, they call it relativity. Real scientists tend to say "evolution" or "natural selection" rather than Darwinism, too.)
in the United Kingdom the term has no negative connotations, being freely used as a short hand for the body of theory dealing with evolution, and in particular, evolution by natural selection http://en.wikipedia.org/wiki/Darwinism