I have an issue with my Canon 70-200 F/4L USM. It is less sharp at 200mm than at shorter range and the objects that are slightly out of focus are rendered twice with horizontal offset. The shutter speed is not the problem, because the effect is similar both with tripod shots and 1/2500 handheld ones. Stopping down the aperture greatly weakens the effect, but it is still visible.

What can cause that effect? I don't know whther my copy is bad or is it my mistake.

The samples below are 100% crops.

Edit: I took test photos with and without the uv filter.

With the uv filter:

Without it:

Both images were taken with tripod from the same place and with the same focus distance (defocused intentionally). The difference is huge and the double-rendering effect is gone without it.