Without really risking any spoilers since the events in Arendt's life are both well-known historically and outlined in all the promotional material for the film, the story arc of the film is as follows. In an initial scene, Mossad and Shin Bet operatives capture Adolf Eichmann in 1960, in Argentina, where he had fled with false documents provided by the Vatican. Some framing scenes show Arendt (Barbara Sukowa) and her coterie of New York intellectuals, including long-time friend Mary McCarthy (Janet McTeer) and husband Heinrich Blücher (Alex Milberg). In conversation we are provided the Jewish Arendt's backstory: She fled Nazi Germany to France where she married Blücher; she experienced a brief, youthful alignment with Zionist groups in Germany; she escaped a camp in France after its occupation; and she engaged in an affair with her professor, well-known philosopher (and Nazi party member) Martin Heidegger (Klaus Pohl). The dialogue, cowritten by von Trotta and screenwriter Pam Katz, is both crisp and
natural, and avoids falling into the easy trap of sounding overly expository -- notwithstanding the obvious obligation of the script to accomplish such.
In a cutaway scene, members of the editorial staff of The New Yorker discuss hiring Arendt to cover Eichmann's trial in Israel, in which a composite character "Francis Wells" (Megan Gay) gets to deliver a delightful and prophetic line to Editor-in-Chief William Shawn (Nicolas Wooseson) -- a missed opportunity to cast Shawn's son, Wallace, as his father: "Philosophers don’t make deadlines."
Both film convention and actual history dictate Arendt attending the trial as a New Yorker reporter. In Israel, Arendt both follows the trial testimony -- both of Eichmann and of various of his "victims" -- and also connects again with friends and colleagues who have moved to Israel and remained Zionist in conviction. These scenes use archival
footage of Eichmann himself, as well as of the testimony of various Jews who survived camps and persecution.
A key point in discussion among the characters, with Blücher often acting as the "conscience of the film" in my reading, involves questions of the legitimacy of the trial, the surrounding legal process and framework, and of the direct culpability of Eichmann in the crimes to which he was a bureaucrat. For example, Blücher at one point objects to the process with the comment "You can't put history on trial. You can only try one man." Indeed, Arendt's observation within the film, and in reality within her resulting book "Eichmann in Jerusalem," is that almost none of the testimony spoke to specific actions by Eichmann himself.
Upon return to New York, after delays and efforts characteristic of a philosopher, Arendt eventually completes her commissioned book-length notes on the trial, which were published both in serialized form in The New Yorker and subsequently, with slight modification, as perhaps her best known book. The publication of her notes on Eichmann's trial led to a great deal of vilification and outrage at Arendt. Her conclusions were both that Eichmann himself, rather than holding any animosity towards Jews simply "did not think" and followed his orders, and even more controversially that without some degree of tacit participation of many Jews in the the process of genocide, the outcome would not have been nearly as bad. Furthermore, she argued, many people acted without grand design, nor even any real intelligence, malice, or ability. In Arendt's characterization in the film, "Once the trains were in motion his work was done. [...] He's a bureaucrat. [There was a] huge difference between the unspeakable horror of the deeds and the mediocrity of the man."