Any idea what the white spots are? Did the board sit in the sun for a long time with bindings on?
First thing I would try is just hot water and dish soap.
If that doesn't work, you could try mineral spirits but it's likely discolouration in the topsheet itself if dish soap doesn't work. If the topsheet is discoloured and you want it to look 100% for wall hanging, the only thing to do is sand the topsheet until the marks come out, and then try buffing.
To sand you'd start with something like 400-600 grit wet dry, and use it wet. Then move up to 1000 grit, 1500, 2000 and finally buff it with polishing compound and a buffer. Topsheets act like automotive clear finishes so generally you can take any car advice with regards to cut and polishing the surface.
On the other hand, I'm planning on wall mounting some of my retired boards, and I think war wounds add character, so I'll just wash them with dish soap and leave it at that.