Hello I just got my new 5DM3 about 4 days ago. It has worked perfectly for me in this short period of time. But this morning I was checking out the accuracy of the outer AF points and all were focusing accurately until I got to the three top 5.6 cross points; if you orientate the camera into the landscape position, it would be the top three points, in the center block of 21, as seen through the viewfinder.
Every once in a while one of the three would attempt to focus, it would appear to move in incrementally a couple of mm at a time and then give up. This would take place say 1 out of 5 attempts, the other two rarely did anything. I tried removing the battery, changing the battery, and use a different lens, but nothing worked.
I have a 24-105L, 70-200 2.8 II and a Sigma 85 1.4. Of course rotating the camera to portrait position made no difference. My luck, both PMI Digital (who I purchased it through) and CPS are closed until Monday morning. I think I will call CPS in Newport News, VA first to see if they would want to take a look at this problem first or try to do an exchange with PMI. Yes, the solution is rather straight forward, but I thought I would post this just out of frustration with a brand new camera.