There's one mistake in the scenes of the Six Gallery reading: In real life, Ginsberg read (because he had, by that time, written) only the first part of "Howl." In the movie, he reads all three parts and its "Holy! Holy! Holy!" addendum, "Footnote to 'Howl.' " This is legitimate poetic license, so to speak. I have no problem with it; in fact, I'm glad the filmmakers decided to do it this way. Franco reads that final section gorgeously. (Nobody taped the Six Gallery reading, but Ginsberg later made several recordings of the poems, and Franco seems to have studied them closely.)
While I'm at it, it's worth noting that the scenes of Franco/Ginsberg speaking in his apartment to an unseen interviewer, ostensibly during the time of the trial, were in fact pieced together from several interviews that Ginsberg conducted in the 1960s and '70s. Each piece is verbatim. Again, legitimate poetic license. Ginsberg wasn't in the country during the trial. He and some Beat pals had gone to Tangier the previous spring, to help William Burroughs edit the novel that would become Naked Lunch(which would go through its own obscenity trial in 1962), then roamed around Paris, Venice, and Amsterdam through the fall.