The surface is folded on itself.
Display surface control points and try selecting one. Most, but not all, are actually two control points which are almost but not quite coincident.
DupBorder, and use the border curve to Split the surface. Four surfaces result which overlap with each other, and at least one of those four surfaces is folded on itself.
@acpavel Was this surface imported or did you create it? If so how did you create it?