The central question in philosophy of science is a meta-scientific question, as would be expected, and it's the Demarcation Problem. You know this, but I'm restating it for observers: What is the difference between science and pseudoscience, and how can it be realized as a repeatable procedure?

Science should be left to scientists, but the interpretation of science is still an individual responsibility.

I do like the joke that career philosophers know no maths aside from arithmetic and about half of Bayes' Theorem.