I don't think I'd be too concerned about the error. The solicitor can go through earlier title Deeds and see if there are any earlier maps plus, unless the other landowner has moved fences and taken possession of the lands, it is clearly not an issue.
It's always best if a concerted effort can be made by all involved to address the issue. If everyone is on good terms, they might all be willing? Of course, as soon as money for lawyers and engineers is mentioned , that might change but worth asking.
mf