Last week, I decided to take the plunge and flip my 5D Mark II cameras with 5D Mark III bodies. The other thing I had been drooling over was the Canon 70 – 200mm f2.8 L II IS lens, so added that to my shopping cart. Today, after shooting less than 100 images on my 5D Mark III, I was stopped in my tracks by an Error 70 message. It persisted even though I changed lenses – the error message was still displayed with both the 24-105mm F4 L Series IS USM and the brand new 70-200. The forums suggest that this is a problem with the CF card, but I formatted this card in the 5D Mark III prior to shooting anything. Since I had this problem with the 5D Mark II, and Canon ended up replacing the motherboard, I’m not convinced that this is simply a write problem with the CF card. Right now, the plan is to exchange the camera for a new body. We shall see… I’ll keep you updated.
Commercial, Editorial and Travel Photographer Susan Seubert 
Bummer. In the short time you have had the Mark III, you probably already noticed how much more agile and flexible the AF is over the Mark II. I went the same upgrade path as you and cannot see myself shooting with the Mark II after using the Mark III.
Hey recently I picked up the mark III and seem to be facing the same issue . . ? what did you do about it? Did canon replace your body?
I had just purchased this body, and was on my way to purchasing a second Mark III along with a 70-200mm f2.8 L Series 2 lens, so the camera store took it back as DOA with no hassle. I’ve been shooting with the two new Canon 5D Mark III cameras and so far have had no issues. This is an interesting thread regarding the error 70 message and the 5D Mark 3
http://www.dpreview.com/forums/post/41021946
Facing same issue. But mine is probably a card fault. The error pops only when that SD card goes in.
I am having the same problem! Never had this problem with any other 5D’s. đŸ˜¦