Canon EOS 5D Mark III Instruction Manual (en)

k Shooting Movies
AEB cannot be used.
Even if an external Speedlite is used, it will not fire.
Continuous still photo shooting is possible during movie shooting. 
However, the captured images will not be displayed on the screen. 
Depending on the still photo’s image-recording quality, number of shots 
during continuous shooting, card performance, etc., movie shooting may 
stop automatically.
If [z5: Movie shoot. btn] is set to [V/
], you cannot take still photos.
If you want to shoot still photos continuously during movie shooting, 
using a high-speed card is recommended. Setting a smaller image-
recording quality for still photos and shooting fewer continuous still 
photos are also recommended.
You can shoot still photos in all drive modes.
The self-timer can be used before you start shooting a movie. If used 
during movie shooting, the self-timer will switch to single-image shooting.