I and many other 5d mkiii owners have experienced the notorious Error 80, where the camera freezes and the only way to unfreeze it is to take out the battery. It's annoying for photographers but potentially catastrophic for film makers, as the current file is lost. There are numerous reports of Eye-Fi SD cards causing Error 80, so if you've only encountered the error with Eye-Fi cards, please discount those errors as this issue is well known.
My thoughts are that if the Eye-Fi cards are definitely causing problems, then perhaps the type of card is a factor. I've had the error twice, both times with Sandisc Extreme 60mb/s CF cards (I don't think there was an SD card in the slot on either occasion).
As well as participating in the poll, please write below and say if you've had the error, and what brand / size / speed / type of cards have been in the camera at the time.