One problem with Popper's falsificationism, considered as pure logic, is: does it apply to itself?
That is, what could falsify the proposition "we should regard as science hypotheses that are falsifiable"?
Or: what could falsify the proposition "we should consider as serious candidates for facthood those hypotheses which are falsifiable and extensive and rigorous attempts to falsify which have failed so to do"?
At this point most philosophers
of science go "oh, fuck it" and get on with discussing the nature of theory - leaving the above argument to the hardcore epistemologists.
Red Rose - if you want to mess with your tutors' heads, try some Bruno Latour -
We have never been modern is IIRC not a bad place to start;
The Parliament of Nature is more fun but as I recall it tends more to assume you've read your Kant. Latour is quite sane, in my humble opinion, totally opposed to the positivists, and if you call him a postmodernist he'll come over and slap you with a baguette
Edited to add: somehow missed the line where ICB suggested applying Popper to Popper