Moldova's new government has an old problem: Transnistria. Can it solve it?
Is it correct to use several it pointing to different things in the same sentence?
Moldova's new government has an old problem: Transnistria. Can it solve it?
Is it correct to use several it pointing to different things in the same sentence?
Sure. It's grammatically correct, but stylistically confusing. It may not be very clear to do so, but it isn't wrong.
Better options: "Can they solve it?" or "Can it be solved?"
Can it solve it?
This sentence is not grammatically incorrect.
Compare:
Can he help him?
Can her mom help her?
It almost always better to be clear. Pronouns can be convenient, but they can also get us into trouble by confusing the reader.
Better:
Can Moldova solve it?
Can Moldova solve the problem of Transnistria?
Can it solve the problem of Transnistria?
Can Tom help him?
Can Ann's mom help her?
So, using only one pronoun, we have two options to the Moldova / Transnistria question. Which is better, and why?
Sentence 1 sounds better because it makes the distant "Moldova" explicit. If we use "it" for the first pronoun, as we see in Sentence 2, the reader might hit a little speed bump and wonder for a moment what "it" refers to. Moreover, we may not want to say "Transnistria" twice--both times at the end of a sentence, which might sound mechanical.