I liked it so far (first 8 episodes). It's good.
But it's not perfect. But it's still good.
Setting the acting, special effects, direction and whatnot -- which are superb: top notch -- aside, let me stick to the physics, logic, and such:
The good:
Their use of necessary "hand-waving" is wonderful. When they do discuss known physics, they don't overstep their bounds. When they discuss General Relativity (GR), Quantum mechanics (QM), multiple dimensions and such, they are refreshingly quite good at admitting, "We just don't know," when it comes to the extremes.
I'm guessing they actually hired some physicists consultants for the script, and the writers/editors thankfully, actually listened to them. I find this really refreshing, since so many other movies, TV series, video games, etc., just throw physics out the window and just simply abuse physics if it helps the plot. If there is technology beyond what we know, 3 Body Problem does quite well at adding the necessary hand-waving to aid in the suspension of disbelief, even among those that understand physics. This is quite nice.
The bad:
I don't think they represent actually how chaotic a 3-body (or n-body) system actually is. [Spoiler alert:] The premise is that the alien world transitions from a habitable environment to a hostile one before inevitably transitioning back to a habitable one again (in somewhat random cycles). In reality, once such a system becomes non-habitable, it'll likely never go back. Ever. And if it does, it's a fluke, not something that can be counted on.
[Spoiler alert:] It seems to be a major part of the premise that the aliens seem not to understand the concepts of lying and fiction. Yet in their "game" there's a hypothetical Isaac Newton and a hypothetical Allen Turing among other hypothetical/fictional portrayals. They are portrayed hypothetically and fictionally. They are put in hypothetical scenarios that are not a true part of history. The aliens can understand that well enough. So what gives? Can they understand fiction or not?! "Make up your mind," I say.