Those "marks" are generally differences in mineralization on the surface. It happens to everything but stainless is reflective so you can actually see it.

I never worry about pasta marks, they're gone with the next use, but if you really, really want to get rid of them now, put some water in the pan with a big glug of distilled vinegar. Cover, heat to a simmer, turn off the heat and let sit for a bit - then wipe out the inside with a good kitchen cleanser.

You will notice pans in use eventually get a sort of dull mineral film on the inside so giving them the vinegar treatment every couple of months keeps them in good shape. If the mineralization builds up too much things may begin to stick to it.

There will be some tiny white spots that won't come out - those are cavitation pits at points where streams of bubbles form and collapse. Like those "scratches" they're microscopic in depth and cause no harm. Again it happens to everything but stainless is reflective so you can actually see it.