Earlier quoted context omitted.
> The point of science is to make a plausible conjecture and try to prove it false. FWIW, and I'm not an expert, but I'd say that the Popperian view you summarise reflects philosophy of science circa 1960's, and things have moved on since then.
I don't want to sound too snarky, but "moved on" sounds like we're talking about fashion... Has modus tollens moved on too? I haven't studied modern philosophy (or Popper), but if there is a concise explanation I'd like to hear it.
As an introduction, Alan F. Chalmers' What Is This Thing Called Science? is good. It covers Popper in chapters 5 to 7 (Introduction & Naive Falsificationism, Sophisticated Falsificationism, Limitations). Then it moves on (as it were) to Thomas Kuhn's The Structure of Scientific Revolutions, Imre Lakatos' Falsification and the Methodology of Scientific Research Programmes (great short read, btw, applying those ideas to maths: Lakatos' Proofs and Refutations), and Feyerabend's Against Method. Chalmers then covers Bayesianism, new experimentalism, the nature of scientific laws, and scientific realism.
They've all pointed out problems with Popper's demarcation criterion. Not sure there's really a good catchy replacement, though. It seems to amount to "it's complicated".
One of the problems with Popper's account is the following: an observation is never about only one hypothesis, but about it and a whole set of auxiliary hypotheses. So, if your observation does not line up with the prediction, do you throw out the theory, or some auxiliary hypothesis? (Eg, Uranus didn't move as predicted, so Newton's physics was wrong. But wait, it was not a problem with Newton's physics, but there was another planet, Neptune.) Quine's notion of a "web of belief" captures that quite nicely - you don't just take one hypothesis, test it, and drop it if falsified, but you adjust the whole edifice such that it becomes coherent again. See [1].