When you do lighting at vertices, you're doing Phong lighting, which is computing a color at the vertices, and then merely interpolating the colors computed at the vertices (i.e., Gouraud shading) across all the pixels in the primitive. If you were to compute the lighting color at each pixel, you'd get Phong shading. Given your scenario, if you move the lighting computations from the vertex shader to the fragment shader, and interpolate the normal across the primitive you should get much better results.
If you make the vertex normal a varying variable and normalize it in the fragment shader, and then do your lighting computations, you should get much better results.