Latest: I've now got my Nest programmed in "range mode", so it's got an upper and lower bound on the desired temperature at any time.

On Monday: the heat was running downstairs and up, which was fine, but the upstairs heat kept running well past the low end of the range I set. It ran the heat up to 81 degrees (I had it set to a range of 70-77F). "Gosh, it's hot", I thought, and went to poke at it to see what was going on, and it then switched to A/C to cool the house back down into the range I'd set.

At least the Nest got daylight savings day right...

I emailed Nest support and so far all they've done is ask "gee, has it happened like this before?" to which my answer is "go check all the historical data from my thermostat that you won't let me get by myself."

Sigh.