The first time I took a picture with the NEX-6 and Soligor 80-200mm lens that resulted in a picture with one side darker than the other, I didn't pay much attention. In fact, I thought it was the lens. Over time, this happened infrequently and I didn't really want to investigate more. But when this happened with the Sony A7, I thought this must have something to do with the camera.
Essentially, when pictures taken at high shutter speed, starting at 1/3200s, you can see that one side of the picture is darker than the other. As the shutter speed goes up, the severity of the darkness gets worse. This is more apparent on vertical shots and shots with a lot of white content. What is happening is similar to using the flash with a shutter speed faster than its rated sync speed; the curtain does not close fast enough and thus leave a portion screen darker than the rest.
Curiously, this does not seem to happen with auto focus lenses from Sony, at least not noticeable. With the Zeiss 35mm f2.8ZA at 1/6400s, there is very little difference across the frame, and with the Sony 50mm f1.8 on the A7 at 1/8000s in crop-mode, there is also no apparent differences. So, this seems to be an issue with just manual focus lenses. It's disappointing, but nothing much you can do.
Sample picture; note dark left side. Taken with Leitz Hektor 120mm f2.5 Projection lens at 1/8000s.