I suppose for me, in the field of education, one of the most challenging areas that I struggle with is the so-called Mozart effect. I have included a link to more information about it below, but basically it is the idea that the performance of students can be improved if they listen to music whilst undertaking tests. I have a number of problems with it, but mostly they stem from how impossible it is to prove or disprove such a theory. I worked for a while supervising trainee teachers as they undertook research projects into education, and a number of them selected this as their topic. The variables are endless: what kind of music, what kind of test, how long the test is, if the test contains new information or just old information and so on.
The central issue is, in spite of the theory, there is very little proof that can actually be used to conclusively support the theory. This makes it a rather thorny issue in the field of education.