That said, the Nest really isn't that great!
That raises an interesting question: what other "dumb" devices can we connect to the internet safely through that same method?
Devices on receiving end are simple enough to be made as secure (or not) as you'd like.
You could even achieve similar isolation even with an optoisolated RS-232 port if the protocol is auditable, non-general, and non-extensible. But good luck actually guaranteeing those things!
Internet access is akin to Turing completeness for programming languages - seemingly beneficial, easy to accidentally obtain, and ultimately a curse.
The only problem I see is that some kitchen appliances have high-pitched beeps that sound really similar. It would take some pattern recognition or something to ensure false alarms. I mean, "You're house is on fire!" is a more serious false alarm than most to get at an important meeting. ;)
A friend has one, and tells me that when his infant daughter screams, it sometimes notifies him that the house is on fire. I wonder if she's learned to game that system...