Canon have released a service notice for the 1D Mark 3 and 1Ds Mark 3, owners affected by the problem can send their cameras in for a free adjustment/fix. From Canon:
We have learned that some EOS-1D Mark III and EOS-1Ds Mark III digital SLR cameras have a problem in the accuracy of the AF (autofocusing) feature. Accordingly, we would like to provide information about the details of this issue and how it can be resolved.
We offer our sincerest apologies to customers using these products who have been inconvenienced by this issue. Canon always strives to provide the highest quality products to our customers, and we spare no effort in our quality management to make sure our customers can use our products with confidence. We hope our efforts will earn your understanding.
If an AF point other than the center AF point is used, focus may become soft.
EOS-1D Mark III and EOS-1Ds Mark III digital SLR cameras
Free AF accuracy checks and adjustments will be provided to affected products. Please contact our Customer Support Center if you own an affected product and wish to arrange for service.
Full details can be found on Canon's Website.