Whenever modems are used to dial into a system, the sounds the modem makes when connecting to other systems, known as the carrier detect, is for a 56.6k modem, which weren't available until 1998. Modems more likely used at the time were most likely 300 - 2400 baud, which didn't feature the screeching sound of later modems.
At the start of the movie, a Telstra phone box is seen. The Telstra branding was not introduced until 1995 so this would have been a Telecom phone box at the time the movie is set. Later scenes in the movie correctly have Telecom phone boxes.
The modems are shown dialing 8 digit telephone numbers using tone dialing in 1989. At the time Australia still largely used decadic pulse dialing and 8 digit telephone numbers were not introduced until 1994.
The railway station where Julian Assange first meets Electra in 1989 is shown with 21st century signs and tactile paving.
The "Are you keeping up with the Commodore?" television commercial ran in Australia in 1985, not in 1989 as depicted in the movie.