Here why the vertical layout of the anisotropic surface will result in a horizontal highlight area when shining lights on it?
I think this is due to the fact that the left shows surface normals, with the colors representing different directions for the normals. So when shining light, the BRDF light is reflected in different directions, but these directions are consistent vertically (since normals are same in vertical lines) but vary horizontally, left to right. This is compared to the isotropic surface where it varies about the same in every direction.
Would this cause problems when rendering since new that direction matters, rendering might give a biased estimate of the surface.
To follow up on the point about the surface normals, anisotropic surfaces have unequal physical properties along different axes. This helped me understand anisotropic vs isotropic a bit more: http://www.neilblevins.com/cg_education/aniso_ref_real_world/aniso_ref_real_world.htm