My big thing was that the science is just wrong.
Most fundamentally, it's not a three-body problem, there are (at least) four bodies: the three suns and the planet.
And the real world isn't going to follow any theoretical solution to TBP anyway. There is atmospheric drag, microscopic gravitational perturbations from the rest of the universe, decreasing solar masses as the stars age, and so forth.
In a system as chaotic as was described, any of these things make the problem intractable.
That said, I did enjoy the description of a digital computer implemented with "people" acting as the logic gates.
Look at my first objection, that the problem described in the book has (at least) FOUR bodies. Yet the idea that it's a three-body problem is pervasive throughout the book.
Surely that in itself is enough to justify some aggravation.
The amount of suspension of disbelief for some questionable premises is very high. e.g. the real-time comms developed by one of the races breaks down one of the key axioms.
"Rainbows End" is must-read cyberpunk IMO. (And of course he wrote "True Names". (In '81!))
The opening of TBP had me hoping -- being a big Neal Stephenson fan -- that the whole book would involve a lot more of the historical context of the early PRC, and then it all went somewhere completely different. I strongly feel that the first bit of the book set in the past is the best part of the entire trilogy.
The idea of Chinese sci-fi in general becoming a thing is very cool though, I think.
I mean, China has censors. I get the feeling it had to be a somewhat veiled metaphor, although it felt extremely obvious too.