It is strongly implied that the Queen had not visited Australia herself since 1954, and nostalgically watches newsreels of that visit. In fact, prior to the Charles and Diana visit depicted on 1983, the Queen had been in Australia in 1963, 1970, 1973, 1974, 1977, 1981 and 1982.
The song that Charles and Diana danced to in Sydney was a cover of "Isn't She Lovely" by Stevie Wonder, rather than a cover of "Can't Take My Eyes Off You" by Frankie Valli as portrayed in the show.
Even though the Royal Australian Air Force Boeing 707 aircraft was masterfully recreated by CGI, the boarding and deplaning scenes were shot using a mock-up of a door from a Vickers VC-10, a British jet airliner manufactured between 1962-1970, which was extensively seen on previous seasons. The Boeing 707 had passenger doors that opened partially inward, and through a complex design with hinged locking panels, that made the door smaller by retracting top and bottom edges, would allow it to be rotated and swung open outwards. These passenger sized doors were only available on the fuselage's left side (forward and aft)- on the fuselage's right side, the doors were much smaller, and a person could not pass through it standing up.
The road to Ayers Rock was sealed years before the Royal visit. And there would be no signs warning about wombats (which do not live anywhere near Ayers Rock).
As the royal entourage are driving to the NSW sheep station where Prince William was staying, there is the cry of the Red Tailed Hawk, a bird that is native to the USA and is definitely not to be found in the NSW countryside.