Chemical vapour deposition (CVD) is a promising method for producing large-scale graphene (Gr). Nevertheless, microscopic inhomogeneity of Gr grown on traditional metal substrates such as copper or nickel results in a spatial variation of Gr properties due to long wrinkles formed when the metal substrate shrinks during the cooling part of the production cycle. Recently, molybdenum (Mo) has emerged as an alternative substrate for CVD growth of Gr, mainly due to a better matching of the thermal expansion coefficient of the substrate and Gr. We investigate the quality of multilayer Gr grown on Mo and the relation between Gr morphology and nanoscale mechanical and electrical properties, and spatial homogeneity of these parameters. With atomic force microscopy (AFM) based scratching, Kelvin probe force microscopy, and conductive AFM, we measure friction and wear, surface potential, and local conductivity, respectively. We find that Gr grown on Mo is free of large wrinkles that are common with growth on other metals, although it contains a dense network of small wrinkles. We demonstrate that as a result of this unique and favorable morphology, the Gr studied here has low friction, high wear resistance, and excellent homogeneity of electrical surface potential and conductivity.