It’s clear that Nest support has access to more state information than is exposed by the thermostat API. I discovered that my system was acting strangely, staying on for a while then off for three minutes, then back on (even well before reaching the target temperature). I spoke with Nest support and while we were talking the agent said "hey, did you just turn off your system?"
He was able to notice that the thermostat had actually lost power while we were talking. Turns out that my furnace was throwing an error 33 (high limit/low air flow) and when it did that it actually removed power from the thermostat. The thermostat is smart enough to stay off for at least 3 minutes in this case to avoid short cycling the furnace.
It would be really nice if I had access to whatever the agent was seeing. This is a relatively serious condition that my application could easily notice, but all the app sees is that the thermostat is not calling for heat.
Any chance we could get read access to whatever the agent was looking at to determine that the thermostat had momentarily lost power?