Black spotting/dust in stainless steel utensils.Is this mildew?

The specks are corrosion pits. Austenitic stainless (aka- 18-8 , 304 , and several other numbers) are notorious for pitting in salt (halides). The 316 and 317 with molybdenum are more resistant but I doubt any cookware producer would go to the extra expense to use these alloys. However, I expect sitting for a couple days with salted water would be needed for pitting to develop. Out of curiosity, check it with a magnet; If strongly magnetic it is likely 13 Cr (410 SS) which would be likely to pit.

This type of black dot corrosion is seen from deposits of osmium dioxide and/or ruthenium dioxide, rare but far too common polluting metals that are often confused as mold. Precious metals, (gold, platinum, etc) after melting, will sometimes show black dot deposits on the bottom if they contain this rare impurity. Osmium contamination will oxidize in air when wetted with a basic solution, such as soap, forming volatile oily crystals of osmium tetroxide which smells of chlorine and very slowly attacks all type of metals leaving black dots. The dots usually form on metal after cleaning with bleach and tends to crystallize into golden (or bright red with amines) square crystals on ceramic/tile surfaces and into metallic flakes on organic/wood/plastic surfaces. black is very non-characteristic and can be due to many other possibilities so try spotting these other signs and pay attention to any chlorine-like odors coming from your homes heater although I realize you will likely never see this post, alas!