I have an A7r with a Sony 16-35mm f4. The zoom ring is quite stiff (in comparison to canon zooms I'm used to). When I zoom the whole lens rotates, albeit very slightly, on the mount. Feels like the lock into the lens mount has a bit of play in it. Is this the loose lens mount issue that I've read about and if so how would I go about fixing it? There seem to be a bunch of aftermarket parts available with various positive/negative reviews and a sony part for the A7s (I believe?) which I don't know how to source.
I just checked it again, firstly we're talking about a very minor rotation indeed, more rock from side to side play than real rotation. I'd measure it as a 0.5mm in total. Secondly it's all my lenses, I only noticed it on the zoom cause it's so heavy it causes it more. Thirdly it's not the mount moving. The lens is moving on it. There seems to be slop in the bayonet mount?
That mount screwed up the registration distance on my camera. It’s only useful if they have fixed that problem, or with certain lenses that can focus beyond infinity.
When I first bought a Loxia lens, I couldn’t get it to focus to infinity or really beyond about 15’. It worked perfectly fine on the other camera I had.
Look for the repair part mount for the a7s. It is the correct dimensions and it is the heavier mount that should have been on the camera in the first place.
The original mount was made of a sandwich of metal and plastic. Absolutely terrible deign as the plastic would deform and allow play over time. The aftermarket and new designs fix that. I really think Sony should have done a recall.
As MJM6 pointed out be careful to test infinity on any lens that get to infinity at the hard stop (well all of them really, but that type will show the problem easily).
One could also just order the A7S bayonet all metal mount as spare part and fixed it on the A7R. That is what I did for mine. Search for "4-536-531-01 Sony Mb N Plate(a(3200)".
HI Beni -- The Sony mount absolutely needs to be changed -- it is the worst mount I've ever encountered in film or digital cameras.
I also went with Fotodiox, in my case the Tough E Signature mount. It solved all my problems of irregular focus and lens rotation and flex. Without it, I probably would have halted my experience in Sony imaging. It turned my "iffy" a7R into a sure thing for image capture. (Still have it! )
I would prefer a Sony part though. 
)