Other mistake: The Sydney harbor scenes have the backdrop of the opera house. The buildings (aka "The Toaster") beside the opera house were not completed until 1998. The film was set in 1976-77.
Revealing mistake: While Frost is on the hotel balcony talking on the phone to Brennan, it is clear the phone receiver is not attached to anything.
Continuity mistake: When Bob Zelnick jokes about wiretapping Donald Nixon, his arm moves from resting on the tabletop to under his chin between shots. (00:39:40)