Plot hole: It turns out in the climax of the episode that there are no bullets left in the gun and Miss Fisher knew it. That would mean then that she deliberately wasted minutes with Simon bleeding out on the floor when Chaim was holding them at gunpoint with an empty revolver, for no discernible purpose.
Other mistake: Miss Fisher takes a handwritten phrase in "ancient" Hebrew to one of the main characters to be translated. The writing is actually in cursive Hebrew and is properly written. While performing the translation however, the "expert" translator holds the writing upside down. He also follows the writing with his finger from left to right. Hebrew is written from right to left. (00:32:00)
Factual error: The whole Egyptian mythos and references are incredibly sketchy: at first it is said that Foyle was born "on the 21st day of Proyet." Leaving aside the fact that Proyet is a season rather than a month and that it simply would not translate automatically into a matching month and day of the Gregorian calendar, it still wouldn't be the 21st of December as stated because Proyet fell rather in a January to May range. Not just that, but in the second half of the episode it's simply identified as "Midsummer", when Proyet was part of Winter and obviously seasons in Australia are the polar opposites of seasons in Egypt.
Factual error: Ignoring the fact that there was no such Pharaoh as "Memses", in the cabinet inventory the missing item is listed as follows: "'Silver stirrup ring, in the reign of King Memses, Dynasty Five, 2600 BC." If it were 2600 BC, it would be Dynasty Three maybe, but not Five, which started just past 2500.
Plot hole: Miss Fisher and Samson have to find the right, narrow, timeframe to sneak into the ringmaster's tent and go through his belongings. But they seem to have an unlimited amount of time once afterwards, since they flat out take the big crate he has in plain view containing all sorts of incriminating evidence, and then have all their time to get to the station to bring the evidence to Jack, compare serial numbers, have a lab check on the vials, even dig up graves, all without Mr. Jones getting suspicious in the slightest.
Factual error: When Miss Charlesworth asks where everybody has gone and Letitia answers, you can get a good view of her desk, sporting above it amongst many photos also an illustration surely out of place in 1928: the "We can do it!" girl created by J. Howard Miller in 1942 and more or less apocryphally identified with Rosie the Riveter, a feminist icon that is quite specific to WW2. (00:22:10)
Factual error: Miss Fisher wakes up at her usual time (not quite cockcrow), receives from Dot the news of the death of her friend, that she heard on the radio, makes her way to the crime scene, and finds there Jack, who is just at that time closing the victim's eyelids. A little strange gesture to be performed, hours after death. Unlikely to work with rigor mortis, too. (00:03:15)
Plot hole: Talking about the murder weapon, the coroner says that the wound was a "horizontal" stab. Nerine's confession is ruled out because she mimics the attack at an angle. Funnily enough though, during interrogation, Jack himself makes a remark about the stage being a spot overseeing the room, and the killer was in fact on stage, and standing. When we see briefly the flashback of the murder, it's clear that the trumpet is way above the head of everyone dancing. So the projectile wound would hardly be "horizontal."
Character mistake: Miss Fisher is shown tumbling her way into Leonard's apartment in a less than graceful manner, with a rather audible thump, and rolling on the floor and to her feet making quite a ruckus. Despite that, Bobby, who is presumed to be alert and on edge since he's breaking and entering, is completely oblivious of her presence. (00:16:30)
Plot hole: At the end of the previous episode Foyle infiltrated the Fisher household and cut the telephone line. However in this episode, taking place just the morning after, no mention at all of the event is made and Bert and Cec off camera phone the police with no anomalies reported.
Continuity mistake: When Miss Fisher is on her knees by the burial site of her sister, the ribbon in her possession is quite different from the one seen at the beginning of the series, which was worn out, with no hint of the shape and color of the blue one shown in this episode and the previous.
Continuity mistake: When Dot is holding Hugh at gunpoint, Hugo Johnstone-Burt is holding a pencil between his thumb and middle finger only when shot from the front with Dot's hands in the foreground. He never has it in the angle behind him, or wider shots. (00:34:40)
Plot hole: The coroner finds the stones "in the nasal cavity" after Miss Fisher's intuition, but he already had examined it in both cases due to the bleeding. Also, it's inexplicable how with the previous case being ruled as the death of a drug addict with no particular findings, the coroner would have still lying around the body to examine for autopsy even when Hugh said the body was found a week before.
Continuity mistake: As the the first conversation between Miss Fisher and her cousin's belle begins, when she mentions "That dazzling party in Charing Cross" she has her hand on the newspaper, but it is on her shoulder at the cut. And then Miss Fisher puts a hand above the hip, changing position at the following cut as well. (00:08:00)