> I trim them with one another mutually and create the network
> patches one by one.

This is your problem, you will not get good results by doing it in this kind of fragmented approach.



> The result should be a perfect shading sphere, no?

No - think of the network as being more like a kind of membrane that is stretching between your wires. If you have a large continuing membrane then that makes for a smooth thing, if your membrane abruptly stops in one spot instead of continuing on then there will be evidence of the stopping area in the resulting shape.

Also see this previous post for some other examples:
http://moi3d.com/forum/index.php?webtag=MOI&msg=1398.19


If you want something to be smooth the best way to do it is to build one large surface for it rather than trying to do it in small separate patches.

- Michael