My big dislike of the Three Body Problem is somewhat meta. The Fermi Paradox solution that it presents, the Dark Forest hypothesis, only "works" in the books because the author made up a bunch of magic technologies and just-so scenarios to make it work. But ever since then /r/Fermiparadox has been overrun with "what about the Dark Forest??" shower thoughts.
I guess it's not so much a problem I have with the Three Body Problem as it is a problem I have with humanity in general.