Had the same problem yesterday. Contacteer Canon Europe today and spoke to a technician. He explained me everyting. The following is the matter: error 80 (and 70 by the way) is given when there is a problem with the memorycard or the battery. The 5d III should be able to handel al kind of cards. The battery best can be a Canon.
if this problem occurs, there are two options: a softwareproblem (firmware) or a hardwareproblem.
In case of software: after resetting the camera, the problem should not come back (or maybe only ones or twice in the future). Resetting the camera: see below.
If the problem comes back offen after resetting, the only option is to sent the camera to the Canon repair centre. The hardware is the problem and needs replacement.
now how to reset the camera:
Lets try resetting your camera using the following steps to try and resolve this issue.
1. Turn the camera OFF and remove the memory card and battery first. Then detach the lens and place it out of the way. Use the camera body cap to prevent dust from getting inside and let the camera sit for 20 minutes.
2. In the interim please clean the lens contacts with a soft, lint free cloth. Use this to gently wipe the lens contacts. Sometimes the lens can lose contact with the camera if the contacts are dirty, so we want to be sure these are free from anything that could possible cause disruption.
3. Put these items back in the camera and turn the power switch to <OFF> and <ON> again.
4. Using the Mode Dial, change from Auto to Creative Zone modes and back testing each, to shoot and note if the issue persists.
5. Try a different Canon EF Series lens on the camera of any focal length.
hope this helps.