Other mistake: The chronology of dates on the teletype printer at the end of the film are not in the correct order. We see "March 13, 1975" followed by "January 3, 1975", which is then followed by two August 1974 dates.
Visible crew/equipment: When Bernstein rushes into the phone booth early in the movie, in the metal edge of the booth you can see a reflection of the camera man.
Continuity mistake: The scene in the film that follows Berstein's interview with the book-keeper, where he is getting all his notes on various bits of paper out of his pockets: there is a Life magazine on the desk in front of Woodward's typewriter. At the start of the shot where Berstein says: "Mitchell, she said something about Mitchell." the mag has gone, then it reappears and disappears randomly in the subsequent shots in this scene.
Visible crew/equipment: When Ben Bradlee (Jason Robards) comes out of his office and yells, "Woodstein!" - calling Woodward and Bernstein to his office - there's a still, wide shot of the entire Washington Post newsroom that stays still as the two men walk from way across the newsroom to the camera, winding their way between rows of desks. As they approach the camera, not only can you see the mike and boom to the lower left of the screen, you can watch it move to follow them as they pass. The entire mike, its cable and part of its boom are on screen for at least five seconds.
Continuity mistake: On the 2 occasions when Woodward's car comes down the ramp from the Paper's parking lot (with the same car double-parked in the lot), as they turn into the street, the same pedestrians are there both times.