Let me start with the positive: the Nest is beautifully designed and easy to install and in every respect appears to be a high quality product.
The negative, for me and my coworkers (the Nest is at my office - it was a gift from a client), is very simple: there are times when you find yourself asking the question, "Why the hell is the heat / air conditioning on right now?"
This never happens with a normal thermostat.
The basic issue, as far as I can tell, is that the Nest learns from people. This seems like a benefit but when you consider the way people behave doesn't work out that way in practice. People get hot because they just exercised; or they get cold because they got a chill waiting for the bus; or they are naturally warmer or colder than someone else; or they're coming down with something, etc.
They change the temperature of the office as a result. And maybe a bit later someone else changes it back, or changes it more, or whatever. So you end up with these weird patterns where the heat is at 19C usually, but for a two hour period in the morning it jumps to 22C, then goes back to 19C, then back to 20C for an hour in the afternoon, etc.
Our previous office thermostat, where you programmed a weekly schedule but could set it to a new temperature for three hours before it went back to its schedule, worked much better in practice.
These days I believe we have the Nest just set to keep things at a constant temperature all the time, which really defeats the purpose and is worse for resource usage than our old thermostat.