It seems a new issue has popped up for the Canon 5dmk3. Multiple people are reporting that there is a light leak through the top LCD panel that directly affects metering. The easiest way to detect this issue is to put the body cap on the camera body as well as cover the viewfinder. Then place the camera in "P" mode at ISO800 and press the LCD backlight button.
As you can see in the video, the shutter speed changes depending on whether the backlight is activated. Similar results are achieved when a flashlight is shone onto the top LCD. Some users are even reporting that direct sunlight or walking into a room with bright overhead light is enough to sway the meter. If you are one of the lucky ones who managed to purchase a 5dmk3, it might be worth doing this little test to see if you need to seek a replacement version.
Remove lens and place the body cap on the camera body.
Place the viewfinder cover on the viewfinder.
(This should theoretically block any light from entering the camera.)
Set ISO to 800 and set the camera mode to "P".
(You should see a shutter speed of around 10 sec.)
Now either shine a flashlight near the top LCD panel area or simply turn on the backlight for the top LCD panel.
This will cause the shutter speed to fluctuate between 5-8 seconds, indicating light leakage.
Video example of sunlight affecting metering:
1st/featured video contributed by Sean Jaeho Yi