I've contacted both Canon and Eye-Fi about this Error 80 issue. Canon doesn't seem to have any idea what the problem is. They basically just say the "don't guarantee" the card will work and then offer to "take a look at" the camera if I ship it to them (which I don't want to do because I'm not convinced they know what the problem is).
I sent Eye-Fi the log file from my card, and they said there were some "errors" and they recommended formatting the card in-camera. So I formatted the Eye-Fi care in my 5DIII. Since reformatting the card in-camera, I seem to be getting fewer Error 80's, but I do still get them on occasion.
Anyone else had any luck finding a solution? Thanks!