Unlike the imaginative explanations given, the definition goes way back to early machinists. After inspecting a finished manufactured or repaired part, the Toolmaker/machinist would1 tighten all parts and screws (Screwed)
2 Use Blueing a blue paint lke stain that stuck easaly to metal (blued) and
3 Put his inspectors mark through the blue paint with a sharp scriber (tattooed)
screwed, blued and tattooed definition by Urban Dictionary