Yep, GKW's got it. Swap those and give it another try. Considering the cases where the lighting is wrong, usually two vertices are correct and only one is off - given that normal n is being applied to vertex n+1 in each "element", this kind of thing is what you'd expect.
I presume in each triangle the normal is the same for all vertices, and that your sphere is made up of a number of "elements"? The bad normals are probably a default normal being applied to the first vertex in each "element", or something similar to that.
Actually, there only difference between the two spheres on the image is GL_FLAT vs. GL_SMOOTH and I would argue that even on the left GL_FLAT image the shading is wrong.
Yep, undoubtedly. The problem is that when in GL_FLAT mode, in each triangle only one vertex's normal will be used. So the errors are that much harder to spot!