Character mistake: The number of victims of the balloon man changes from seven to eight between the initial scene where he is introduced and where Holmes finds out the identity of the original balloon man.
Character mistake: Sherlock states that Sean Figueroa has "such blue eyes" even though he has brown eyes. (00:39:05)
Character mistake: When looking at the car near the start, Sherlock says he can tell by the pattern of the bullet holes that the gun was fired in 3 round bursts. But when we saw the attack earlier, the gun fired in bursts of different lengths.
Character mistake: They are in the interrogation room questioning the fiancé of the scientist Natasha when the captain says, "the blood we found at the scene of your fiance's murder, it didn't belong to Bobby Cordero." The characters name was Benny Cordero, which the captain says correctly a few lines later. (00:33:25)
Character mistake: Clyde is a tortoise, but Joan, after finding Sherlock, put him in her bed, brings him down and calls him his "pet turtle." (00:14:08)
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)
Character mistake: Sherlock and Joan are looking at video footage of a restaurant called "La Porte Blanc", which is incorrect French. The right way is "La Porte Blanche."
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)
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.
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."
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.