Stucco is not intended or designed to be waterproof (as in the moisture barrier for your house). There should be a moisture barrier of either a Tyvek type material or black felt paper(roofing type). If the nails are visible on the inside of the walls then the moisture barrier has been compromised and needs to be repaired/replaced. Your doors will continue to have moisture damage because the moisture is inside the walls. Wet insulation will harbor mold growth and the mold will digest the wood and kraft paper facing on the insulation. Call the builder if you can locate him/her. It was built to fail. Sorry. (Home Inspector, Mold Remediator, General Contractor)