Dynamics of surface roughness during polycrystalline pure iron electrodissolution is investigated at constant current density by means of ex situ atomic force microscopy. The scaling of the local surface width reveals that surface kinetic roughening is anomalous with both the exponents of local roughness, α_loc, and growth, β, close to 1 pointing out that interface evolution is unstable. We show that this anomalous unstable behavior results from the development of a faceted surface structure exposing different crystal orientations. The presence of smooth faceted walls is consistent with the value α_local~1, whereas the difference in the dissolution rates on the different crystallographic planes account for the nonlocal effects causing the unstable growth. Results are discussed in the context of a recently reported anomalous scaling which accounts for dynamics of self-organized depinning models displaying faceted interfaces. The influence of the electrode potential on the dissolution rates of the different crystallographic planes, along with its effect on the mobility of metal adatoms, are discussed to be behind the complex behavior of local roughness when the current density is varied.