Pretty much every "event" on the show was "inspired by" some real thing or event. But the show is deliberately a work of fiction, an "alternate universe" where everything real was dialed up to eleven.

I was the historical consultant for the second season of the show, and spent a lot of time helping the writers map out the "template" events that they would "dial up to eleven." It was a very collaborative process, the best case I've experienced of writers and historians actually working synergistically (and not a case of the historians just providing almanac-like information).

I have written blog posts that go along with the show and talk about some of the "inspiration" events that most people don't know about. They are all tagged with the show's name on my blog ("Manhattan (show)"). For example, there is actually considerable historical speculation about whether Oppenheimer's mistress, Jean Tatlock, committed suicide or was murdered. In another example, the military head of the Manhattan Project did contemplate locking up one of the troublesome scientists in an internment camp. There were issues with prostitution; there were issues with local judges; there were several unusual deaths; there were numerous spies. But again, the show is not meant to be history, but history-inspired fiction. (It is a shame it got cancelled after two seasons — there was much more yet to do!)