Here is a haAretz article on what's controversial with her writings on Eichmann. That controversy was made into a film.

For her writings on Totalitarianism she had no access to Russian language sources. She relies on the sayings out of date with what she is using them for not sourced and taken, as google reveals, from news papers, from Trotskist pamphlets etc.

In her «Reflections on Little Rock» she voiced opposition towards Black Suffrage in US America.

Her support for Heidegger was controversial because Heidegger would refuse to show remorse for what he had done in the Nazi regime.

To lift with from an old post of mine, historians have generally moved on significantly from the concept of 'totalitarianism'. Arendt's Origins of Totalitarianism remains a foundational work but one that has been largely superseded by the last few decades of research.

To be blunt: plenty of scholars now criticise the totalitarian framework as deeply flawed and unsustainable beyond the broadest level. This criticism tends to flow along two avenues:

• On the grounds of simple historical accuracy, the typical charges of totalitarianism tend not to stand up to scrutiny (rule exclusively through terror, monolithic party structures, etc). We simply know more about these societies than Arendt did in the 1950s; it's hard to talk in such broad terms when we have so much more information on, say, the jungle that was the Nazi state or the social flux of Stalinist industrialisation.

• More importantly, an isolated comparison of just the USSR and Nazi Germany (to say nothing of other candidates) doesn't reveal many common features. On such important questions as the role of the party there were real differences between the two. It's only when a third, hidden, element is introduced (ie Western democracies) that it becomes possible to ignore these differences and treat both states as the same. It's a false comparison.

Beyond Totalitarianism is a strong set of essays that demonstrates the real limits to the thesis by pointing out the contrasts between Nazi Germany and the USSR. Dictators and Dictatorships, which provides an introduction to the literature surrounding authoritarian regimes, focuses less on specifics but still paints the totalitarianism framework as once-useful-but-now-outdated.

Which is not to say that the Origins of Totalitarianism is not worth the read, it's obviously been massively influential, but keep in mind that it's no longer current.