The influence of microstructure on the manifestations of the Portevin-Le Chatelier (PLC) effect was studied in an Al-Mg-Sc alloy with unrecrystallized, partially recrystallized, and fully recrystallized grain structures. It was found that the extensive grain refinement promotes plastic instability: the temperature-strain rate domain of the PLC effect becomes wider and the critical strain for the onset of serrations decreases. Besides, the amplitude of regular stress serrations observed at room temperature and an intermediate strain rate increases several times, indicating a strong increase of the contribution of solute solution hardening to the overall strength. Moreover, the grain refinement affects the usual sequence of the characteristic types of stress serrations, which characterize the dynamical mechanisms governing a highly heterogeneous unstable plastic flow. Finally, it reduces the strain localization and surface roughness and diminishes the difference between the surface markings detected in the necked area and in the region of uniform elongation.