Revealing mistake: It is revealed that the ghost apparitions come through thanks to projection over falling sand, but that's not the trick used in the actual movie shoot: no sand is falling and accumulating on the floor in the last ghost apparition (when we can see the floor for a while) and in the second apparition (to Miss Fisher backstage) the line of sand was in the wrong direction for it to act as screen.
Factual error: Miss Fisher and Dot browse several issues of Table Talk, an actual Australian publication from the era depicted, and with the exact same font for the header. The cover layout is not at all like the original (it's contemporary and sexier) and they obviously glued newly printed covers to modern paperback magazines, because the actual Table Talk had very limited foliage (around 24 pages) while the magazines shown here are one inch thick. Moreover, a "June 15 1908" edition is mentioned, which was a Monday. Table Talk was a Thursday magazine.
Continuity mistake: Miss Fisher serves a dumpling to Dot and is complimented by Lin about her dexterity with chopsticks, which she is holding in two different ways between shots. Not just that, but when she asks about "the skirmish" a few moments later, the chopsticks become a cup. (00:13:00)
Character mistake: The general idea in the first part of the scene with Dot and Miss Fisher at the balcony would be that she is so flustered by the handsome actor, she was wearing her binoculars backwards. But Ashleigh Cummings is in fact at first looking through the binoculars the proper way, then turns them around, and puts them the wrong way. (00:05:00)