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.