Can't update Cyanogenmod on AT&T Galaxy S III
The message is basically telling you that you don't have the correct bootloader version on your device; specifically, you most likely have an older ICS bootloader rather than the Jelly Bean one. You can read a bit about this on CyanogenMod's Google+ page, and the CM Wiki page for the S3 succinctly notes:


  Going forward, CM10.1 is no longer compatible with ICS bootloaders on this device. Please update or else you will get assert failures in recovery.


You'll need to upgrade to a newer bootloader. This carries some amount of risk since it's one of the few instances where you could potentially brick a device, but the risk is still generally pretty small.

I found links to the newer AT&amp;T bootloader on XDA that will work with CM 10.1. You can flash them using Odin or Heimdall by following these instructions:


  
  Go here http://forum.xda-developers.com/showpost.php?p=41503727&amp;postcount=13716
  Put phone into download mode and then open Odin.
  Choose the PDA slot and then select the correct file for your device (AT&amp;T is LK3)
  Hit start and wait until its finished. 
  Done