What is the secret? :) POSSIBLE SPOILERS!

First there is the secret behind the secret. Joe Mitchell identified with Gould, despite being a writer who was able to maintain a middle-class existence, in contrast to the homeless Gould. At some point he observed that "Joe Gould is me." Probably, in part, feeling that he could have descended into madness if circumstances had been different. To some extent, Mitchell was willing to believe that there was no Oral History and that Gould was a fraud because it helped him feel better about feeling (justifiably or not) like a fraud himself. Especially after he promoted the idea that Gould was writing this book and then covered it up when he later concluded there was no book. Finally, in 1964, Mitchell decided to come clean and admit that there was no book. At that point, however--and this is the secret behind the movie's secret--people contacted Mitchell to say that there was, in fact, a book, and they had part of it. It turned out that, obviously, being homeless, Gould could not keep an enormous manuscript with him, so he gave parts of it to various people. No one has, to this day, found enough of it to say it really existed, but enough to say that Mitchell's description of it as completely non-existent is inaccurate. There is a story about all of this in the 27 July 2015 issue of The New Yorker.

Some things that the movie may or may not deal with that are mentioned in the recent New Yorker piece: Gould was a stalker--after a number of people (perhaps his stalking of Mitchell is shown in the movie). One of his victims was Augusta Savage, an African-American sculptor. Gould had very peculiar ideas about race (albeit not entirely out of synch in an era when lots of people did) and was anti-Semitic, but he claimed to love black people, and, in the case of Ms. Savage, this love took a carnal turn. She was completely not interested and had a dickens of a time shaking him. Finally had to leave New York. Another thing is that Gould was friends with some famous literary figures, notably, Ezra Pound and e.e. cummings. Also, though this might belong on another thread--and not having seen the movie I don't know if they mention it, but Gould wrote articles in his younger days for The New Republic and other prominent magazines; so it isn't as if Gould never wrote anything that might make someone think he was writing a book.

Another bit of (potential?) trivia: I have not confirmed it yet, but I suspect that Joseph F. "Joe" Gould was related somehow to Col. Robert Gould Shaw, the man portrayed by Matthew Broderick in the movie "Glory."