Bruce, I've just been playing around with a mesh to see if I could replicate the effect displayed in your images. I discovered that when I selected a vertex and then went to Polygons->Normals->SetVertexNormal[] I could recreate the problem. Simply by choosing an arbitrary value.

To fix, I selected Polygons->Normals->VertexEditTool simply manipulating until it conformed to the shape of the topography and was a rough average of those vertices surrounding it.

Simon.