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.
Plot hole: It's stated multiple times that the Semper Apex server room is protected from wireless signals, but Sofia's team sneaks in and plants a "ghost jack" with a wireless transmitter on it, which they say is slaved to an IP address. Except that wouldn't work in the server room. There'd be no way to get a signal to or from it.
Episode #4.1 - S4-E1
Plot hole: When DCI Roz Huntley kills Forensic Coordinator Tim Ifield the crucial piece of damning evidence is her DNA under his fingernails after scratching her arm. Problem being, at the time of his murder, he was wearing surgical gloves. (00:56:40)