A Y/Mo multilayer coating, optimized for top reflectivity at λ=12 nm, has been nano-inspected after long-term operation at the in-house soft x-ray laser. The surface and optical inspections were complemented by electron microscopy on cross sections, prepared with focused ion beam technology. A factor of 2.5 loss of reflectivity in the exposed area (ca. 30% relative loss every 100 shots), with concomitant nanoscale photodamage and particle fallout, was found. The x-ray-laser-induced damage extended as deep as 250 nm beneath the surface and as wide as the millimeter spot size.