@ Axilrod: So it is the card that is at fault here in that it should be reformatted before each shoot? Are there specific cards less prone to these type of failures?
I'm just starting to do videos and I'd like to avoid these problems. Thanks.
The big problem usually comes when using SD cards to record a video. The 5D MK III is not UHS-1 compatible, so it cannot write to SDHC UHS-1 cards at full speed.
CF cards should not have the issue.
There is some misleading information also being given here when someone says "Format the Card before using it"
There are two types of format. In Camera regular format will not erase existing files on a card, it just marks them as available to be overwritten. HOWEVER - they must be erased before being written to, so when you try to record, the camera must first erase a block of the card and then write to it. That is very slow.
What you can do is perform a LOW LEVEL FORMAT. That erases a card completely, and then writing to the card is much faster since it doesn't have to erase before writing. That's why new cards work fine, and then later they cause problems after the blocks have all been used.
CF cards overwrite cells much faster, and are much preferred to SD for video or any application where you need fast writing.
Now there are UHS-1 cards. Cameras that are compatible double the bus frequency for reading and writing, so with a 6D, for example, overwriting a fast SDXC UHS-1 card should be ok. Even so, its better to have several cards and do a low level format on them before reusing them for video.