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 #1.1 - S1-E1
Other mistake: The team blow the flat door in (no. 56/59) with charges applied to the door. When Arnot arrives, the door is intact on the floor, complete with the door number, including the loose 6/9. This is pivotal in revealing that they have the wrong flat! Stairwell sign indicates flats 50 - 59. Regardless of which way they approached, they would have passed other flats and observed the door numbers. (00:02:28)