In the ballroom Phryne is wearing a gown with shoulder straps - when she follows Lofty outside the gown now has cap sleeves (it is obviously not a removable jacket and she didn't have time to change)
When Phryne climbs up the wall to escape the police in Jerusalem, she is wearing blue pumps. When she strips off her robes to reveal an evening gown a few minutes later, she is wearing gold high heels.
There is supposedly a Greek inscription which they seem to pronounce as 'Tombus Dakyron', meaning 'Crypt of Tears'. They are close with 'Dakyron', as 'Dakryon' (note: different sequence of letters) is Greek for 'of tears', but 'Tombus' appears to be a made-up word, which looks more like Latin, but isn't.
When Phryne and Jack find the tip of the obelisk at Shirin's deserted village, the word for Greek word for God is supposedly on the tip. But word is not Greek; the first letter is not Greek at all, and the third letter is a delta, not an O as they pronounce it.
The night just before a solar eclipse, there's a full moon in the sky.
At the ball, the photographer has the viewing hood on the back of the camera open. This is unnecessary as having a film holder or magazine in place would prevent the use of the ground glass for composing or focusing. Also the camera appears to be a 1940's era Crown Graphic with the flash handle mounted on the wrong side of the camera.
When Phryne is arrested and taken to Sir Montague, the arresting officer hands her pistol to Sir Montague whereupon he opens the revolver and you can clearly see all six rounds have pin dimples in the center of the rounds, meaning they've been fired. When he empties the rounds on the desk, the audio is for empty brass cartridges clinking, but the bullet is still in the cartridge and would have made a thud noise.
The opening titles say this is set in 1929. But they are flying around in De Havilland DH82 Tiger Moths, which first flew in 1931.
The whole 'collecting honey' story. The girl goes way up to a hilltop to collect honey, in a dry arid location where there are no flowering plants for the bees to collect pollen. She collects it with no protective clothing, and yet does not get stung (however, some beekeepers are able to collect honey without being stung, and there are honey bees without stingers as well). And what she gets is ready processed honey, no honeycomb at all. What brilliant bees those must be.
At Lofthouse Manor, Phryne addresses Forsythe as Superintendent. His actual rank is Assistant Commissioner, which Phryne would know because she had met him earlier.