It appears Canon released firmware version 1.2.3 for the 5D Mark III on 2013-10-30.
According to the Canon CHANGELOG:
Firmware Version 1.2.3 incorporates the following improvements and fixes.
- Fixes a phenomenon in which the flash may not fire depending on the timing of when the shutter button is pressed.
- Fixes a phenomenon in which the AF microadjustment value may change.*
- Fixes a phenomenon in which the LCD monitor may show a line of false color along boundaries of high contrast.
- Fixes a phenomenon in which the histogram of a LiveView image is incorrectly displayed when an HDMI cable is connected.
- Enables the brightness of the camera’s LCD monitor to be adjusted even when an HDMI cable is connected.
*The phenomenon listed in 2 was addressed with Firmware Version 1.2.1, and has been further improved with Firmware Version 1.2.3.