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Here is the final fixed result:

Shading

You need to click on the Tangent menu in the material settings and select a Tangent node. Make sure Radial is selected it its settings. Play around with the Axes: to figure out which one to use.

Gandalf3's image from here.

Modeling

Your mesh is covered in triangles (not good). From the .blend file that I downloaded, this was my process:

1. A twice to select everything.
2. Alt + J converts many tris to quads.
3. Ctrl + Tab, then 3 to enter Face Select Mode.
4. Alt + RMB while hovering over one of the edges around the outside rim to select this face loop:

5. Ctrl + I to Invert Selection.
6. X > Faces to open the Delete menu and delete Faces.
7. Ctrl + Tab, then 1 to enter Vertex Select Mode.
8. Alt + RMB while hovering over one of the edges in the topmost edge loop to select this edge loop:

9. F to create an N-Gon face.
10. Ctrl + I to Invert Selection.
11. F to create an N-Gon face.
12. Tab out of Edit Mode.

Here is the fixed .blend file:

P.S.

This is not included in the .blend file, but if you want less spotty anisotropy, you should use these settings in the Properties panel > Render tab.

They produce this result: