Driven by the perspective of large-scale, high-quality graphene production via chemical routes, the investigation of electrochemical anion intercalation between the basal graphite planes has seen a renewed interest among the scientific community. At relatively high electrochemical potentials, when oxidation occurs, graphite electrodes undergo significant anion intercalation processes. The latter swell the uppermost graphite layers (i.e., graphene sheets), reduce the interplane interaction and favor the graphite delamination in liquid. Different intercalation stages are observed in a perchloric acid electrolyte, which are usually interpreted in terms of different perchlorate penetration depths. Nonetheless, the understanding of the morphological changes occurring at the electrode surface during the different intercalation stages is still not completely clear. We combine different microscopy techniques including optical, scanning electron and electrochemical atomic force microscopies to analyze the morphological evolution of the graphite surface at different length scales as a function of the applied electrochemical potential. Whereas both carbon dissolution and blisters affect the surface on the micrometer scale as soon as intercalation starts, we find that the graphite surface is cracked on the sub-millimeter scale only when intercalation at a higher potential is reached, inducing a significant aging of the electrode surface.