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For analysis of the cause of Canon TS-E lenses being soft in one corner or along one edge when used on the A7r, there are a few thing that might be tried to help determine the cause.
One possible cause that Fred left out is that the particular TS-E lens you are trying does not lock accuratly at zero tilt. Besides knowing that the lens works well on a Canon full frame camera, you could also do a check on the A7r by rotating the tilt part of the lens 180 degrees and also changing the shift to the other side, and see if the soft location moves to opposite after the rotation, or stays in the same place on the A7r. If it moves, the lens may not be accurate for its zero tilt lock. If the soft location stays in the same place on the image, then there is some tilt coming in at the adapter or in the camera.
For the issue mentioned above by Fred in number 3, that relates to the microlens design of the camera sensor working with high angles of incidence, there is a check that should show if that is the problem. If you see the issue with a maximum shift to one side, try reversing the shift to maximum the other way, and see if the problem moves to the other side. If it moves, then the microlenses may not be capable of accepting the higher angle of incidence that light from a shifted lens has. I know that Canon put in a lot of work a while back to get the corners of their full frame sensors to work fairly well with wide angle lenses, and perhaps Sony just did not allow for really wide lenses. But it also seems like Sony would know better, and they also need to make their own wide lenses work well. And actually Sony lenses with the shorter back focus will likely have even sharper angles of incidence than an adapted Canon lens of the same focal length. What is the widest native Sony lens for the A7r, and are there reports of how well it works in the corners?
I hope you guys get this all figured out, so I know if I should consider an A7r, or should just wait and save up a bunch of money to buy what ever Canon comes up with for high resolution.