Is the stainless steel pot pitted by salt water a food safety problem?

Chemically the pits etched in your pot are the absence of the stainless steel material that makes up the pot. In other words the white spots you're seeing are where a small amount of the stainless steel has been removed from the surface of the pot, much like it had been scraped off. So the pits are completely harmless because they're not actually any kind of chemical substance.

Chemically what causes the etched pits to appear is that the chlorine from the salt attacks the passive film of chromium oxide that normally protects the surface of stainless steel. Stainless steel gets its corrosion resistant properties through the addition of chromium. When exposed to oxygen the chromium in the steel oxidizes and forms a very thin layer of chromium oxide on the surface the metal. This layer prevents oxygen from going further into the steel preventing it from further oxidation (rusting).

Normally stainless steel isn't harmed by salt dissolved in water or by the chlorine found in tap water. However things are different when a grain of salt sits at the bottom of a pot. It will dissolve into chloride ions (along with sodium ions) that are concentrated against a small spot on the surface of the pot. What exactly happens then isn't entirely clear, I've read conflicting descriptions, but the reaction seems to reinforce itself causing the chromium oxide layer at that spot to be removed. This exposes the steel underneath to damage by both chloride from the salt and oxygen dissolved in the water.

(The Chemistry Stack Exchange has a question on how chlorine attacks stainless steel if you want a more scientific explanation.)

There's really nothing you can do or need to do fix the spots at the bottom of your pot. You can't remove something that's not there. A new chromium oxide layer has already formed over the pits and your pots is as corrosion resistant as before.

I too have seen this in my SS cookware and have tried the Barkeepers trick also. I do worry however that the aluminum cladding underneath the SS is now exposed at can/will leach into my foods. Any comments on this. A little more research on this and I came across this; so it appears to be okay but could change somewhat the taste in acidic foods.

From: https://www.cooksillustrated.com/how_tos/6390-is-aluminum-cookware-safe

The amount of aluminum that leaches into food, however, is minimal. In lab tests, tomato sauce that we cooked in an aluminum pot for two hours and then stored in the same pot overnight was found to contain only .0024 milligrams of aluminum per cup. (A single antacid tablet may contain more than 200 milligrams of aluminum.) Our science editor reports that the consensus in the medical community is that using aluminum cookware poses no health threat.