The scientific method
As I said, it exists only in an abstract sense. On the ground, research rarely looks like the model of the scientific method presented in the textbooks. In addition, the demarcation problem has never been solved. This doesn't mean, however, that there aren't clear-cut cases of science and pseudoscience. (Say, astronomy vs. astrology.) The real trick is in identifying what lies in the gray areas in between these cases. One way of conceptualizing scientific methods that I think is much closer to reality is Imre Lakatos' concept of research programmes. Each program is its own sort of mini-paradigm working with its own set of assumptions and empirical results.
"On the ground, research rarely looks like the model of the scientific method presented in the textbooks."
Preaching to the choir! Ha! I rarely see how many of the core philosophy of science concepts, like the difference between induction and deduction, help when figuring out what an IR spectrum is telling you. Well, I suppose it does if you get into the highly abstract, but in actual research it's pretty useless.
Well, deduction and induction are logical concepts, not based in philosophy of science per se, although the latter makes heavy use of them. I think many of the more specialized areas of phil of sci can be useful to primary research though -- for example, work by philosophers of biology on units/levels of selection.