I can't speak for your other coins but those are not copper spots on that coin, that's some kind of foreign material. To me it looks like it might be fabric fibers - red lint in other words. It might blow off, it might need to be rinsed off, but in any event I suspect it could be removed fairly easily.
I agree with Doug, give it a distilled water rinse/soak followed by an acetone rinse/soak and see if that helps...remember, DON'T RUB IT!!!