Writing from my phone, please excuse typos.
The biggest negative right now is lots of third party enemies starting to attack you. Rogue Thoraxians, as well as I believe 4 different kinds of animal nests. 5? I can't remember for some reason.
The idea of a global planet mood actually went away, as that turned out to be confusing and not really needed. Instead of it being truly global, or even Empire-wide, there is now a city stat called planet rage. This is how passed the planet is at that specific city.
This is a lot more interesting because you can try to keep your planet-angering activities to just certain cities of yours, thus giving you yet one more reason to diversify your cities.
Since it's literally a rage meter now, there's no way to make the planet be "negative rage" toward a city. But! The other races (except Thoraxians) also incur planetary rage on their cities, so you can use that to your advantage against your foes. In theory you might be able to get the planet pissed off at a race by brokering certain diplomatic or trade deals. I don't have that aspect designed in yet directly, but some of the existing stuff could be manipulated a bit to cause that. I'll be sure to add more direct options (one layer of indirection rather than two, I mean) in later in the month.
As for making the planet like you, that's actually a different thing entirely. This goes beyond rage of the planet at cities, and instead has to do with your overall social progress levels. When you go for a social progress victory, that actually is you working to take over the position of favored planet race from the Thoraxians and make that yourself instead. This process can only begin once you already have all the other social levels unlocked and then you choose to go for the Transcendence victory condition. As soon as you start taking levels in that category (there are 4), the planet starts liking you a whole lot more, but the Thoraxians start to HATE you. And pull out all the stops.
So there's two main mechanics involving the planet as a being. Rage at cities, and then the Transcendence victory path. Actually there are some other things as well, but they don't involve any direct numeric quantification of some elements that of the planet's mood. But two other Victor conditions put you straight at odds with the planet in the worst way. And based on discussions here on the forums I plan to have the planet's manipulation of the climate be something that is actively visible and that the races' attempts to modify the climate all run up against. That was a pretty cool idea, but I've not specced that fully yet.