In the concluding section, we claim that Locally-Irregular 2-Edge-Colouring remains NP-complete when restricted to planar graphs, essentially because 1-in-3 Satisfiability is NP-complete for planar formulae. This is a wrong statement, since, in our NP-completeness proof, we have a main gadget that, essentially, needs to be connected to all vertices of a planar graph. Clearly, adding a universal vertex to a planar graph does not preserve planarity; from this, we get that connecting the gadget as intended might break planarity. Thus, the statement is wrong, and the complexity of Locally-Irregular 2-Edge-Colouring for planar graphs remains open.