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for scratches, I found QUIXX
tested on xbox https://www.youtube.com/watch?v=vJWAvQwkbW4
Ok 
I think the back of the Z3 is fairly sensitive to micro-scratches, by cons there are no scratches on the front. which is why I posed the question.
This is particularly unfortunate from Sony, the back glass should be the strong point of the device not the weak point.
the first day I got my Z3, I ended up with what appears to be a semi deep small scratch. I mean I didn't even put it in my pocket or anything, I was only holding it. must have been my ring that made the scratch but it would have been done with next to no effort. even with my cover on I sometimes take it off to find some randome new scratches :s it's strange.