What you will take will depend on your particular program and the departmental requirements for the M.S. degree. A smart move (I found) was to take as many Ph.D-track required courses that I could add on, because I was not 100% certain if I wanted to pursue M.D. or Ph.D. at the time. I would not attempt to take UG courses while in graduate school. Although you may be permitted to take them, they likely will NOT be counted towards your undergraduate GPA (if that is what you are worried about). If I had taken undergraduate courses in gradual school, they would have only counted towards my graduate GPA (there would have been no, separate, "undergraduate" GPA) - furthermore, undergraduate courses had to be "OKed" by the graduate school and the department, or they would not count at all, and a graduate student could only take a certain number of undergraduate credits per semester, for credit.
Perhaps my experience will give you a bit of insight into what will help you on your path to med school. I finished my M.S. in Microbiology and Immunology a year prior to matriculating to medical school. I completed the degree in 1 year, and took the "Ph.D. track" courses, in case I changed my mind and decided to go Ph.D. instead of M.D. I ended up taking 17 credits my first semester, and 19 the second semster. My courses included graduate-level micro and immuno department coursework in: immunology and lab, human and microbial genetics, pathogenesis of infectious disease, a course in bioterrorism agents and emerging infectious diseases, an advanced immunology tutorial, and 3 of the micro&immuno department's seminar/journal club offerings - "general micro/immuno", "science policy", and "biological threat agents and emerging infectious diseases."
In addition to my departmental courses, I also took the Ph.D.-track courses that ALL first-year biomedical science Ph.D. students must take (in case I decided to get my Ph.D. instead of applying to medical school; in which case I'd already have a year completed), which included: graduate-level biostatistics, biochemistry, cell biology, molecular biology, and seminar courses. I also was able to take a 5-credit graduate physiology course during the second semester that counted towards my degree. I did not take undergraduate courses, but this was an option for some programs (for example, many of the excellent science policy courses were offered only at the undergraduate level. M.S. students were expected to complete an extra project in order to have it count as a graduate course).
Like UG, your graduate GPA is important. If you have 3 semesters over which to space your courses (1.5 years), I would probably take it easy the first semester, in order to gauge course difficulty, and then ramp it up over the last 2 semesters. I found graduate school to be vastly different from undergrad, and it took some adjustment. As for taking undergraduate coursework as a graduate student - personally, I would advise against it, unless you need the background in order to pursue further graduate coursework in that subject (for example, a bio major starting a bioengineering M.S. program may need to take those engineering and math courses at the undergrad level, if they have never taken them before, prior to completing the graduate-level coursework), or for reasons in the example I offered in the above paragraph. You are in graduate school to pursue a higher level of education in a particular subject of interest - not to fill in the gaps of your undergraduate education. There must be less expensive and time-consuming ways to do the latter.
One more note: I also struggled a bit in undergrad, and ended up with a sub-par UG GPA/science GPA. However, I really had the chance to shine in graduate school. Even though your UG GPA matters substantially, if you really perform some outstanding work in grad school, I believe that a poor UG performance can be (somewhat) overcome. Also, developing relationships with faculty members is much easier in grad school (because they see you more as a peer and less as a student), leading to some excellent LOR opportunities. I would give up on trying to pad your UG GPA, and start over with your grad GPA as a clean slate. It worked for me.
Good luck in grad school!
