A printer detects inoperative inkjets during printing of three dimensional objects. The printer includes an electrically conductive substrate onto which a printhead ejects building material in a test pattern. A plurality of electrically conductive members arranged in a pattern corresponding to the test pattern are moved a predetermined distance towards the substrate so ends of the members either contact the surface of the substrate or the building material on the substrate. An electrical current source coupled to the substrate produces a current in those members contacting the substrate. Thus, the inkjets corresponding to the members in which an electrical current is produced are identified as inoperative and the printing of an object can be suspended to take remedial action with regard to the printhead.