I have both the 5D Mark III and Mark II (and the original 5D before that) The AF the Mark II is accurate but very slow compared to other high end dSLRs. The center point on the Mark II (in my experience and I worked with 3 of them) was always quite good, the outer points not so good.
I just got my Mark II's back from their annual clean and check. I asked Canon to check the AF and discovered the AF was greatly improved when they came back.
I think (and this is just my theory) that as cameras are used bits of dust and crud get into them, including into places that may block the AF sensors. (Again this is just a theory of mine but it's one I've had for awhile.)
Dust or crud blocks access to the sensor and this will degrade AF performance. I think it might be why some outer AF positions work better than others. In my Mark II's the AF performance varied from sensor to sensor and camera to camera. Now they both perform properly. The center point, perhaps because it is cross type sensor, doesn't seem as susceptible to this problem as the outer points.
I want to stress that this is not fact. It's just a theory I have based on watching AF performance change on the many 5D series cameras I've had through the years.