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.
Character mistake: Sherlock tells Odin at the bridge where he framed him for his own murder that they are opposite poles of a magnet - they repel. That's wrong - opposite poles attract each other.
Character mistake: Sherlock states that Sean Figueroa has "such blue eyes" even though he has brown eyes. (00:39:05)
Continuity mistake: While playing the piano in Justin Guthrie's apartment, he is bare handed. In the next scene when he gets up to point at the blood, he is wearing gloves. (00:24:12 - 00:24:42)
Enough Nemesis to Go Around - S3-E1
Factual error: The 1-ton electromagnet is supposed to have moved only the bullets without affecting the steel elevator car at all. This is impossible.
Character mistake: The American Flag is hung improperly on the wall. The Flag's union (stars) should be at the top, to the observer's left, but it's to the observer's right. (00:06:38)
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)