A hardware fix said to be coming in the next month from Canon should help Canon EOS-1D Mark III users.  The fix is meant to solve poor AI Servo focus prediction when tracking a moving subject.  We will update the blog with information as it becomes available in the future.
Rob Galbraith.com has been tracking this issue for months and has a very in depth log of the investigation into this problem.

Beginning on October 17th, Canon began to inform users of the Mark III of the coming fix.  Users will be able to send in their camera to Canon to have the sub-mirror adjusted.  "The sub-mirror - also called the secondary missor - is a tiny mirror behind the main mirror that passes light down to the autofocus module in the base of the mirror box.  The adjustment procedure may included the swapping of one or more parts that make up the sub-mirror mechanism, though the sub-mirror component itself will not be replaced." - robgalbraith.com

October 2007Technical documentation