The aim of this work is to study the strain localization and the fluctuations in shear bands using molecular dynamics simulations. We show that: (1) The localization of frictional dissipation acts as a precursor mechanism of failure; (2) Buckling of chain forces may explain the finite width of shear bands; (3) The building and collapse of stress columns lead to stress and dilatancy fluctuations in the critical state; (4) Vorticities in the displacement field assisted by rolling between the grains reduce the dissipation with respect to the expected value of simple shear. The implications of these rotational modes in the Cosserat theory and in the study of tectonic activity are outlined.