Perhaps it's just me, but I find all my lenses do fine on my Mark III, and in fact, seem better than on my Mark II. My 70-200/2.8L tended to vignette more on my 1Ds2 than I'm experiencing now. In designing the new chip, Canon made a concerted effort to improve light efficiency with the micro lenses and spaceing of the photo sites. I've seen the difference.
I just shot an editorial, available light (ISO500-640), shooting with my 50/1.4 at f2.8. Normally, the 50, by some at least, is not considered sharp. I found that not to be the case. If anything, it was the accuracy of the autofocus that hindered some of the lens performance. Given sharp, dead-on focus, the body peformed well, in regards to lenses. A few shots I did with the 24-70/2.8, also wide-open.