Factual error: Beckinsale is a US Marshal - the service in question does indeed have someone stationed at Amundsen-Scott South Pole Station. However, this station is not in the United States (The US has no territorial claim in Antarctica). As such Marshal Stetko has only such jurisdiction as is enforceable by the US's stated intention to prosecute its citizens when they go home. The enforceability of that is another story, but it's not the only circumstance under which the American government does this sort of thing. So, these arrangements may not be very persuasive even if you are an American. If you are not an American, Stetko has absolutely no authority whatsoever. Certainly not enough to ziptie an Australian to a chair, as she does in one scene. The Station is in every practical sense an American base, but they have no solid way of making their jurisdiction stick, especially against non-Americans.
Other mistake: The Union flag in the comms room at Amundsen-Scott base is upside down. They did get the one flying outside right, though.
Plot hole: The UN agent boards a 50-year old Russian cargo plane, has to ask the pilot, Delphy, where the hatch is, and yet immediately accesses the triggering mechanism, down to knowing which of the connectors is for the explosive bolts. How likely is that?