I've been doing some testing with my 5DmkIII, primarily testing various lenses and comparing files vs. a 1DmkIII (that has been pretty reliable with AF) and the same lenses. I can say the 5DmkIII is proving to be the most reliable Canon body I've owned for AF (at least since my EOS 3 camera, but that was film so it was harder to evaluate for critical focus). Anyway, after about 200 shots, I've found 2 photos that were clearly out of focus, just missed it. The rest are either right on, or within a reasonable range that the photo would be entirely usable for most purposes. As compared to my 1DmkIII, which the best I've ever acheived was about 90% accurate, and as bad as about 75% accurate. My 5D original was worse, and my 7D is probably worse, though I've never really tested it since I never use it for really critical photos.
One other thing, the image quality of the 5DmkIII in mRAW mode compares favorably to the 1DmkIII at ISO 200-400 (obviously, the 5DmkIII will be much better at much higher ISOs, so I haven't tested these two at higher ISOs yet). This impresses me, because I've always felt the 1DmkIII has extremely good IQ at those lower ISOs, on a pixel per pixel basis, probably one of the best, maybe?! (I believe Rob Gailbraith has stated as much.) This is very encouraging to me, as I'm going to part with my trusty old 5D, and am now feeling like I'll probably replace my 1DmkIII with a 2nd 5DmkIII body one day (or maybe another body not announced yet?), once I've absorbed the cost of the first one anyway.
BTW, the main lenses I've focused on testing were the 24-70 (first version, of course...a rather good copy, knock on wood) and my trusty 24-105, both were tested wide open. The 24-105 barely beats out the 24-70, but not by a very appreciable difference, and that was on either camera, the 5DmkIII or the 1DmkIII. I was encouraged by this as I can freely use either lens on either camera without worry.