Continuity mistake: When the mayor of San Francisco signs the new 'gay rights bill,' he puts the pen to paper with his left hand in the far away shot. When the camera cuts to the close up of him signing the bill, he's writing with his right hand.
Continuity mistake: When James Franco leaves Harvey, his dog is sitting on a chair next to him. The dog disappears in the next scene, but is back seconds later. There is not enough time for him to jump off and back on.
Visible crew/equipment: A boom mike is visible in the camera store the last time Harvey is seen there, hanging over his head.
Factual error: When Harvey sets up his very obvious "SOAP box" and gives his first speech, modern vehicles can be seen parked along the curb behind him, most obviously the small US Postal van and UPS truck. A little later, a 2000s era black SUV is at the curb when Harvey steps out of his camera shop.
Factual error: The character is given an effeminate voice. Harvey's voice was not at all effete.
Factual error: Dan White did not attend Harvey Milk's birthday party at City Hall as in the movie. It never took place.
Audio problem: During the birthday sequence, the singer's voice is not in sync with his lips when he is seen on the background. He sings when there's only music sounding and no voice.