What's the difference between "Распространять клевету в отношении Китая" and "Распространять клевету о Китае"? Is there a slight difference in meaning there?
What’s the difference between “spreading rumors concerning China” and spreading rumors about China”?. Pretty much the same difference is in Russian.
In other words, there’s not much of a difference. Any language possess certain level of redundancy, one can speculate that there’s very subtle connotational differences, but I’d rather not.
However “распространять клевету в отношении кого-либо/чего-либо» sounds too official, bureaucratic even. You most probably hear something like this in TV news but not in a casual speech.
Well, to be more strict, it rather be "клевета на Китай", not "клевета о Китае".
The first sounds OK I guess, since it implies that a whole country (China) is falsely accused of something, so the formal language (в отношении) is expected.
The second sounds slightly incorrect and quite informal, for the most grammatically correct form is 'клевета на Китай'. But since it's not a person who is involved, but a whole country, the first seems to sound not bad at all.