I originally asked this question on gamedev, but none of the answers helped to solve problem, and I still have no clue what is the real cause. I didn\'t see anything about r
i believe that what you are seeing may really be caused by the precission. You correctly calculated that the floating-point coordinates should be pretty enough, the problem is the hardware is not using floats to lookup the textures. The texture interpolator units do have considerably lower precision (don't know how is it today, but it used to be as low as 16 bits on older GeForce cards).
So ... how can one exceed interpolator precision? By using large texture coordinates (many repeats) on a large geometry, which is exactly what you are doing. Remedy? Subdivide your geometry to be using smaller texture coordinates (you can shift texture coordinates in integer steps so they are closer to 0).
Here is a screenshot of how extreme it can look like (i weren't able to reproduce the error on my GeForce 260, but it is clearly visible on my Tegra 2 tablet, as shown in the image below).