This paper is devoted to the Study of the influence of the electrochemical kinetics on the microscopic structure of a metal-electrolyte interface dissolving through anodic dissolution. The effect of intermediate adsorption reactions, single or multiple dissolution paths, and passivation processes, are investigated in terms of surface roughness and adsorbed species organization along the interface. Computer simulations results are compared to theoretical predictions developed from a macroscopic kinetic description based on probability functions emulating the classical mass balance equations. A linear approximation to the relationship between the spatial and temporal scales of the dissolution front allows an analytical investigation of its structure. The consistency of simulation results with the predictions of a rather simple model is promising. Consequences of interface structure are also addressed, in particular, the feedback action oil the electrochemical kinetics when non-linear reactions are involved. In that case, quantitative departures of reaction rates from the mean field approximation can also be modeled by considering the local correlations between adsorbates, thus raising the important role of chemical ordering oil the interface evolution. Conclusions obtained from this theoretical investigation are in the line of recent observations.