The newspaper article says Sam is missing from the USS Enterprise. The ship he is on when sailing into Sydney is the USS Marvin Shields (FF-1066), and when responding to the peace protesters is the USS Lockwood (FF-1064).
Air raid sirens are heard going off in several scenes. Sydney did not have any functional air raid sirens after 1945.
The time the nuclear device hit Jervis Bay is quoted on the radio in Eastern Standard Time. The film is set mostly on New Year's Eve and New South Wales has had summer daylight savings since 1971. The time should have been quoted as Eastern Daylight Time or Easter Summer Time.
It is unclear why they leave the empty Sydney Opera House, which has one of the deepest basements in the world extending 120 feet below ground, for the crowded and relatively shallow Martin Place railway station.
When Brendan is on his knees singing into the vacuum accessories, the boom mic is clearly visible on the upper left hand side of the screen.