Update: I am about to start implementing this. Please speak up in case of objections, better ideas, and so on.
I propose the creation of one or two somewhat general tags to be used for some of the questions now tagged pedagogy:
general-pedagoy: for questions touching upon pedagogical considerations and problems of a general nature, i.e., not specific to mathematics. Please note that some aspect of the question should still be related to mathematics.
mathematical-pedagogy: for questions on general considerations and problems of teaching mathematics, i.e., issues specfic to teaching mathematics yet relevant to various contexts and courses.
Maybe one, then named general-pedagogy, could suffice with a slightly broader description then. But at the moment I am leaning towards having both.
None of them should be used too freqently, but only if it is really a rather general question.