Cooking pots overheated
Yes, they are still safe to use. You aren't going to be able to heat them to the point where the metal starts breaking down — at least, not without starting a fire. 

Your only concern might be if your pots have a nonstick coating, which can be damaged above temperatures of 500 F and begin emitting noxious fumes. According to DuPont:


  The fumes that are released by overheated [Teflon coatings] can produce symptoms referred to as "polymer fume fever" — flu-like symptoms that are relatively quickly reversed in humans.


The residue you're seeing is likely just some mineral deposits that, as mentioned, can be removed with vinegar or other food-safe solvent.