Arendt was a defender of Heidegger even in the post-WWII world.

But moreover, Heidegger didn't just "turn brown". He saw NAZIism as a potential realization of his philosophy. Such a belief definitely influences my view of Heidegger. Any summary of Heidegger's philosophy and it's problem naturally either involves a lot of simplification or is book length. For book length critiques, I'd recommend The Jagon Of Authenticity by Adorno. My simplification of Heidegger's weakness is that he among a number of philosophers criticizing the lacking of authenticity/awareness/true-being/etc in the modern world in isolation. Such critiques tend to fall for political movements promising the violent reconstruction of tradition - such as NAZIism but limited to that. Michelle Foucault's despicable endorsement of Ayatollah Khomeini on the eve of the overthrow of the Shah is quite similar Heidegger's turn.