Continuity mistake: At end of the episode, when Sherlock leaves Detective Bell outside the 11th Precinct, Bell had a book and an envelope of which Bell puts the envelope in his pocket leaving the book, the next shot shows Bell turn and throw the envelope in the trash and the book disappears. (00:39:15)
Continuity mistake: Early in the show, when Sherlock is making eggs, he adds milk and sets the jug down. The camera shifts to Watson and back to Holmes, which shows the jug missing. Watson then walks around Holmes and sets the jug down in the spot it was in previously.
Other mistake: When Sherlock and Watson look at the coffee order from the trial it has the names of the 4 jury members who robbed the vault. Not the original men that did the robbery.
Unfriended - S7-E11
Character mistake: Odin Reichenbach talks to Sherlock about "doing the irrevocable", but pronounces it "irrevOWEcable." It should be pronounced "irrevacable" in both British and American English. He's supposed to be a highly intelligent, highly educated person - not a mistake he should make.
Suggested correction: Not necessarily. A lot of people have strange vocal tics where they pronounce a certain word in a certain way, usually without even realizing it. My grandfather was a smart guy, and he always mis-pronounced "toilet" as "ter-let."
On the Scent - S7-E9
Continuity mistake: Sherlock and Marcus visit a suspect's house. There are a bunch of cell phones on a console. One is gold with the name "'Mandy" on it. In a wide angle shot the gold phone is by itself next to some other black phones. Next closeup shot you see the gold phone is on a different position behind some other phones, and a green phone is added to the bunch. (00:18:40)
Red Light, Green Light - S7-E4
Other mistake: The crash at the start is staged - the semi truck is driving at 20/30mph, is T-boned by the van, and stops instantly. No screech of brakes, no allowance for the driver's reaction time. In the shot of the impact it's moving at barely walking pace, hence being able to stop so quickly.
Factual error: The number plate on the black cab is GW22 ARY. This won't happen until the year 2022. (00:28:20)
Character mistake: When they've worked out that the kidnappers were changing flood maps, Harlan says he "doesn't get why anyone would mess with flood maps in the first place." Looking at the maps it's blatantly obvious that the reworked flood zone excludes a chunk of land, and given property prices in New York it doesn't take a genius to figure it's at least connected to real estate, insurance, etc. Harlan is demonstrably a genius, and could certainly have figured that out for himself.
Continuity mistake: Just before Sherlock and Detective Bell enter the dead professor's office, both are putting on gloves. Sherlock puts on the left first and has partially put on the right. As they enter the office, Sherlock still hasn't put the right glove on at all - he's just starting to do so. (00:05:30)
Continuity mistake: Watson came to Mycroft's place, spent the night and was awoken by Sherlock (this episode) the next day. Somehow she had a nightie and a brand new outfit. (00:00:05)
Factual error: Holmes shows an epinephrine auto-injector, but it is only a training device without any needle or medicine: 1. The real epinephrine auto-injector has a transparent housing to enable the user the check of the solution inside the cartridge. The shown "device" has only a grey, opaque housing, as the training device has. 2. The real epinephrine auto-injector has an orange-colored needle guard in the form of a hollow body. The shown "device" has only a finned dummy. (The real epinephrine auto-injector (single use device) is sold with a training device (reusable) to let the user practice the application once or multiple times). (00:25:50)
One Watson, One Holmes - S3-E19
Character mistake: Sherlock says "Cherchez la femme" but pronounces "femme" as "fem" rather than "fam." In earlier episodes, he has been seen speaking fluent French, and so would be unlikely to make so basic an error. (00:16:30)
It Serves You Right to Suffer - S5-E9
Continuity mistake: When Joan accuses Agent Whitlock of gathering intel to Rip Off/ambush/rob the gangs, a woman enters the hall behind her. Moments later, The Woman disappears having never walked past Joan or Agent Whitlock. She didn't open any of the doors in the hallway either since she was walking straight down the hallway.