I'd be worried about any internet-connected IOT device in my home. It the very least it can snoop on traffic. The Nest in particular could a) use it's motion detector to report if you are home b) harass you through temperature changes (and maybe even gaslight you by not showing them) c) maybe overload something (itself?) and cause fire?
That's just what I can come up with sitting here and having no in-depth knowledge. I am sure actual security experts could come up with more scenarios.