While You Were Sleeping - S1-E2
Other mistake: When Sherlock was slapped, he later says he was surprised because the girl who slapped him was a "lefty." Then he rubs his right cheek and says it's leathery from all the slaps he's gotten, while the left is soft. This is backwards - anyone hitting him with their right hand would hit his left cheek.
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)
Other mistake: Before the security guard is killed, he turns around and faces the direction of the camera. He is killed, and the camera backs up to reveal 6 men standing there. The security guard would have seen the men and he had time to react to them, but did nothing. (00:32:50)
Episode #5.6 - S5-E6
Other mistake: The caption at the end says that Steve was cleared of any wrongdoing in the shooting of "Police Constable Martina Tranter." She was actually a Police Sergeant.