The paper discusses spatial discretization techniques for the bidomain model of cardiac electrophysiology. A detailed error analysis for the conduction velocity is presented, which shed light on several questions and previous result in the literature concerning mass lumping and current interpolation methodologies. Based on the results of the analysis, we introduce a stabilized scheme with artificial conductivity, which tends to correct the conduction velocity on coarse grids. Finally, a weighted mass lumping scheme is shown to be super-convergent on uniform grids.