This dog actually belongs to a relative of a former coworker of mine. We were techs at the same hospital until she left a few months ago. She posted this story on her FB wall and solicited the thoughts of her former colleagues, and this is what I wrote:
"It's awful but I can definitely see how it could happen and how a dog like Mia might be more at risk than average. She's a big dog and it seems like she was reasonably healthy aside from the neuro issues. She was given what was supposed to ...be an overdose of anesthetic. But every patient is different. A fatal overdose for one may not be so for another. And if the dose was lowballed or if some of the drugs went SQ, it's not too hard to imagine how it could have happened. We've seen healthy animals die during routine anesthetized procedures despite every reasonable effort to keep them alive so it shouldn't be surprising that an animal could survive euthanasia. The line between life and death is really more of a continuum when you are that close to it, so it's definitely possible to end up on the side you didn't intend. Mia was basically anesthetized and woke up, pretty much like she would have if she'd gone in for a dental. It just wasn't the plan here.
I admit I worry about this sort of thing myself. I hope I've never put an animal in the freezer who was still alive, but I can't say for sure. The absence of an audible heartbeat, visible respiration, and palpebral reflexes are definitely reliable signs that someone is dead, but human senses can most certainly fail to detect subtle signs.
Having said all that, it sucks that something with such ridiculously long odds had to happen to someone you care about. I hope they're doing okay. And I still miss you!"
From what I've seen on my friend's FB page, it does seem like the veterinarian's response to this situation left something to be desired. But this is just my perception, from posts made by understandably upset family members.