Like for everything else, the horrors of ReactJS are seen when:
As for the biggest limitations: I can't answer that question, I have not met significant limitations in the way I use React. It doesn't mean it is perfect, and there are other projects solving similar problems more elegantly.
React is not a framework, there is a very wide ecosystem around it. You can write applications where React only plays a small role (taking care of the view), and therefore can hardly become the limiting factor.