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.