I believe there are no correct, unaddressed criticisms of Karl Popper’s epistemology (Critical Rationalism – CR). If I'm mistaken, I'd like to be told. If others are mistaken, I'd like them to find out and take an interest in CR.
I've found CR criticism falls into some broad categories, with some overlap:
The people who heard Popper is wrong secondhand but didn’t read much Popper and have no idea what CR is actually about. They often try to rely on secondary sources to tell them what CR says, but most secondary sources on CR are bad.
The pro-induction people who don’t engage with Popper’s ideas, just try to defend induction. They don’t understand Popper’s criticism of induction and focus on their own positive case for induction. They also commonly admit that some criticisms of induction are correct, but still won’t change their minds or start learning the solution to induction’s flaws (CR).
The falsificationism straw man, which misinterprets Popper as advocating a simplistic, false view. (There are some other standard myths too, e.g. that Popper was a positivist.)
Critics of The Logic of Scientific Discovery who ignore Popper’s later works and don’t engage with CR's best ideas.
Critics with points which Popper answered while he was still alive. Most criticisms of Popper are already answered in his books, and if not there then in this collection of Popper criticism and Popper’s replies. (I linked volume two which has Popper’s replies, you will want volume 1 also.)
If you believe Popper is wrong, then: Do you believe you personally understand CR? And have you looked at Popper’s books and replies to his critics to see if your point is already answered? If so, have you written down why Popper is mistaken? If not, do you believe someone else has done all this? (They understand CR, are familiar with Popper’s books including his replies to his critics, and wrote down why Popper is mistaken.)
Whether it’s by you or someone else, you can reply with a reference to where this is publicly written down in English. I will answer it (or refer you to an answer or get a colleague to answer). Here is what I expect in return: if your reference is mistaken, you will study CR. You were wrong about CR’s falsity, so it’s time to learn it. If you would be unwilling to learn CR even if you agree that your referenced criticism of CR is false, then you shouldn’t have an opinion on CR. If you still wouldn’t want to learn CR even if all your objections were wrong, then you either aren’t participating in the field (epistemology) or shouldn’t be. (I have nothing against lay people as long as they are interested in learning and thinking. I do have something against people, whether lay or philosophy professors, who state their opinion that Popper is wrong but would not be willing to learn about Popper even if they found out their negative beliefs about Popper are false.)
If you believe one of the many criticisms of Popper is correct, but you don’t know which one and don’t want to pick one, then you are not treating the matter rationally. It’s unacceptable if your plan is, on having one criticism answered, to simply pick another one, and repeat indefinitely. You’re welcome to have one good reference which makes multiple important points, but you don’t get to just keep referencing different critical authors repetitively (as each one fails, you pick another) while not reconsidering your own beliefs. You need to stick your own neck out – as I do. If I can’t answer a challenge to CR I will reconsider my views.
If you want to bring up a couple criticisms at the start, which are written in different places, but you won't add any more later, then that could be reasonable – but provide a brief explanation of why it's needed. In this case where you want to bring up multiple points by different authors, I'd expect you to be referencing specific sections or short works, not multiple whole books. E.g. you could reasonably say you have 3 criticisms of Popper, chapter 3 of book X, chapter 7 of book Y, and paper Z.
Alternatively, if Popper is mistaken but no one has actually written correct criticism (including you), then how do you know he's mistaken? Maybe he's not!
Note: I'm interested in criticisms like "Popper's idea X is false b/c Y.", not like "I wasn't convinced by Popper's writing on topic X." (The second one is compatible with Popper being correct, and is too vague to answer.)
Broadly, the reason criticisms of CR fail is the critics do not understand CR. Having read a lot of Popper criticism, I can report this theme is nearly universal in my experience. (There is one problem with CR, which sometimes comes up, which I fixed.) CR is hard to understand because it disagrees with over 2000 years of epistemological tradition. And people in general massively underestimate the effort it takes to understand ideas well. (People seem to think they can read a philosophy book once and understand it, but that isn’t how it works – study and discussion are needed to clear up misunderstandings.) Pointing out misunderstandings of CR, with quotes, is one of the typical ways I answer CR criticisms.
Secondarily, Popper criticism often fails because the critic is much less smart and knowledgeable than Popper (one of the world’s best ever thinkers). I think people can get smarter and more knowledgeable if they make the effort, but most people don’t make that effort in a serious, persistent way and put a ton of time into it. I will not use this as an argument against any particular criticism. It’s not an argument, but it is a part of the world’s intellectual/scholarship situation which I think matters, and it helps explain what’s going on. It’s hard to criticize your intellectual betters, but easy to misunderstand and consequently vilify them. More generally, people tend to be hostile to outliers and sympathize with more conventional and conformist stuff – even though most great new ideas, and great men, are outliers.
See also: CR reading recommendations.