Anybody who thinks Popper provided useful insights into how science proceeds should read David Stove's Scientific Irrationalism. Stove tears Popper to shreds. (He also defends inductive probabilism so he'd be agreeable to seekers of the Way.) Popper's theory never gained much traction in philosophy (inductive probabilism, even Bayesianism, has garnered more serious interest) but certain popularizers who happen to be Popperites (notably Brian Magee) have given him a false sense of prominence in their works. The particular philosophies of science that scientists espouse at any given time are subject to fad; logical positivism, instrumentalism, Kuhn's revolutions, they've all been popular at some point. Personally I think this gives credence to the idea that none of them have anything useful to say.
New Scientist on changing the definition of science, ungated here:
I'm a good deal less of a lonely iconoclast than I seem. Maybe it's just the way I talk.
The points of departure between myself and mainstream let's-reformulate-Science-as-Bayesianism is that:
(1) I'm not in academia and can censor myself a lot less when it comes to saying "extreme" things that others might well already be thinking.
(2) I think that just teaching probability theory won't be nearly enough. We'll have to synthesize lessons from multiple sciences like cognitive biases and social psychology, forming a new coherent Art of Bayescraft, before we are actually going to do any better in the real world than modern science. Science tolerates errors, Bayescraft does not. Nobel laureate Robert Aumann, who first proved that Bayesians with the same priors cannot agree to disagree, is a believing Orthodox Jew. Probability theory alone won't do the trick, when it comes to really teaching scientists. This is my primary point of departure, and it is not something I've seen suggested elsewhere.
(3) I think it is possible to do better in the real world. In the extreme case, a Bayesian superintelligence could use enormously less sensory information than a human scientist to come to correct conclusions. First time you ever see an apple fall down, you observe the position goes as the square of time, invent calculus, generalize Newton's Laws... and see that Newton's Laws involve action at a distance, look for alternative explanations with increased locality, invent relativistic covariance around a hypothetical speed limit, and consider that General Relativity might be worth testing. Humans do not process evidence efficiently—our minds are so noisy that it requires orders of magnitude more extra evidence to set us back on track after we derail. Our collective, academia, is even slower.