I don't know if schools will tell you automatically if your file is incomplete or if they will inform you by phone if you call.
I'd generally look at 2 things in determining is a letter was science or non-science: 1)how does the professor know the student and 2) what is the professor's department.
Generally, professors know students through courses or labs. If the course is classified as BCPM or the professor knows the student through interactions in a lab, then it is a science lab (ok, so psychology labs are labs but not BCPM- that can go either way but I'd say science given the context).
If a faculty member is a member of the Bio, Chem, Physics, Math or similar science department, then the letter is a science letter. (eg. Assistant Professor of Biology) Non-science letters come from faculty members in the English Department, Philososophy, Foreign Languages, Music, Journalism, Art, Theater, Law, etc. The social scineces are a bit of a toss up but I'd call them non-science because generally the "science letters" are expected to come from the natural sciences.
Almost everyone I know who teaches biomedical ethics is in the philosophy department.... Having a letter from a Professor of Philosophy is a slam-dunk non-science letter.