Rob Galbraith analyses the Canon 1D Mark III autofocus capabilities and finds that, under certain conditions, it has a few problems. Briefly, these are that the camera has difficulty acquiring focus initially in a multi-frame burst, it's sometimes unable to properly track a moving subject, focus can shift slightly but constantly at times when the subject isn't moving and tracking a subject that's moving somewhat erratically, and the camera is far too quick to shift focus elsewhere.
I always avoid buying the first batch of any electronic product, irrespective of the hype and the necessity, precisely because of teething problems. I hope these autofocus problems can be resolved quickly by Canon.
The full analysis can be found on Rob Galbraith's website