Is there a term for someone who "can see multiple perspectives"?

open-minded

broad-minded

There are more synonyms under the link for "broad-minded".

Perspicacious

Clear-minded, astute, perceptive, discerning (Chambers)

Interestingly, perspicacious has etymological roots which are similar to perspective./

I would suggest the following:

comprehensive

comprehending mentally; having an extensive mental range or grasp.

of broad scope or content; including all or much

objective

not influenced by personal feelings, interpretations, or prejudice; based on facts; unbiased: an objective opinion.

The expression, a critical thinker could fit. It is an invaluable academic skill which once learned is never forgotten.

It means not taking what you hear or read at face value, but using your critical faculties to weigh up the evidence, and considering the implications and conclusions of what the writer is saying.

On Critical thinking.org there is a cool wheel which lists the characteristics of critical thinking.

and finally on Wikipedia we have this (emphasis mine):

Critical thinking is a way of deciding whether a claim is always true, sometimes true, partly true, or false. It can be traced in the West to ancient Greece with its Socratic method and in the East to ancient India with the Buddhist kalama sutta and abhidharma literature. Critical thinking is an important component of most professions [...] Critical thinking employs not only logic but broad intellectual criteria such as clarity, credibility, accuracy, precision, relevance, depth, breadth, significance, and fairness.

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