2:02 into the show, a newspaper shows the date as Thursday, February 7, 1929. It is indeed true that February 7 was a Thursday in 1929; however, at 20:14, a calendar on the kitchen wall behind Hugh Collins shows February with 7th on a Saturday. A 7th on a Saturday would only be true in 1929 if the month was either September or December, or true for February if the calendar year was either 1925 or 1931.
In the final scene where Jack and Phryne walk near Melbourne's Palais Theatre, you can see a poster for comedy rock band Tenacious D, which was performing there around the time of filming.