High potential purified Trametes trogii laccase has been studied as a biocatalyst for oxygen cathodes composed of layer-by-layer self-assembled thin films by sequential immersion of mercaptopropane sulfonate-modified Au electrode surfaces in solutions containing laccase and osmium-complex bound to poly(allylamine), (PAH-Os). The polycation backbone carries the Os redox relay, and the polyanion is the enzyme adsorbed from a solution of a suitable pH so that the protein carries a net negative charge. Enzyme thin films were characterized by quartz crystal microbalance, ellipsometry, cyclic voltammetry, and oxygen reduction electrocatalysis under variable oxygen partial pressures with a rotating disk electrode. New kinetic evidence relevant to biofuel cells is presented on the detection of traces of H2O2, intermediate in the O-2 reduction, with scanning electrochemical microscopy (SECM). Furthermore the inhibitory effect of peroxide on the biocatalytic current resulted in abnormal current dependence on the O-2 partial pressure and peak shape with hysteresis in the polarization curves under stagnant conditions, which is offset upon stirring with the RDE. The new kinetic evidence reported in the present work is very relevant for the operation of biofuel cells under stagnant conditions of O-2 mass transport.