Spots on kitchen wall

Sounds like the screws/screw holes. Not sure why they are turning purple. Take a small nail and tap it into the spots and see if there are indeed screws in each one. Could be rusting screws maybe?

Should be fairly easy to fix. Scratch out the spots and apply drywall compund with a putty knife and repaint. You have any pics?
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.