Spots on kitchen wall

This is your answer. You've got moisture in there, which is causing the screws to oxidize. You could just hit it with some Kilz, and stop the coloration from bleeding through, but that won't stop the mold from growing under the sheetrock. Get in there and hit it with bleach, after you've solved your moisture issue.

Thanks.. I'm just trying to figure out where the moisture would be coming from. Roof leak? Laundry room?

I would think that if it was a lot of moisture, there would be a lot of mold on the wall since these spots have been there for 3+ years. Also, there are no such spots on the opposite wall inside the laundry room.