Ok, I took and analyzed your climates compared to my favorite map of earth's climate zones. Supercontinents in earth's history have had more seasonal differences in precipitation than most of the world today currently experiences, so I tried to keep that in mind.
Overall, I was pretty impressed with your climate assignments. I've done this before and I understand some of the science behind the considerations in planetary climatology. I drew out some of the currents, assuming that your planet has similar tilt and spin as ours, and I think your assumptions are fairly accurate.
I do have a couple of suggestions based on this image I made of your map:
Your climates are painted with a pretty broad brush, and are very stratified. That savannah on the western edge of the continent is about as wide as the US. Mix things up more. Zoom in on areas and make them more detailed (you're probably planning on doing this anyway).
I think the areas circled in purple should be more mountainous, not mediterranean. Compare the California coastline, which butts up against the Rockies, to the Mediterranean on Earth, which has relatively few mountains around it.
The stripes on the east coast (green circle) are pretty delineated; I think that one biome (I'd pick continental) would dominate, with others creeping in along the edges - and they would take the effects of the mountains into effect more.
That savannah in the center-south (orange circle) bugs me. Depending on the mountain ranges' sizes surrounding it, it could range from continental to desert, but I don't think I would ever choose savannah. Not the whole area, anyway.
That's all for now; hope that gives you some thoughts for improvement. They're just my thoughts; take them with a grain of salt. I think you could defend your current climates without much difficulty, honestly. Just depends on the details of your world.