When Moriarty is getting ready to steal the Crown Jewels, the position of the gum he places on the glass to hold the diamond changes between takes. Sometimes it is by the bottom of the "E," sometimes it is to the right of the "T."
The scenes shot on the roof of St. Barts are physically different from the street view of the same area. In the rooftop scenes, the front ledge of the building is about twenty feet wide. From the street the ledge is around 80 feet wide.
As Moriarty is writing "Get Sherlock" on the case of the Crown Jewels, one shot shows that he has already written the "She-" of Sherlock and the next shot shows him just starting to write it.
When Sherlock and Jim are at the roof top and Sherlock laughs and comes back to Jim to tell him what he missed, it's clearly visible that his scarf is a little messed up, but when the shot is focused on him 2 seconds later, the scarf is perfectly straight.
In the courthouse scene, where Moriarty asks security to reach into his pocket, she does so and places a piece of gum into his mouth. A trained court security officer would not do this, as this would place them in a position of disadvantage. In addition, as Moriarty was in custody, his clothing would be searched and contraband such as gum would have been disposed of. Gum especially is a security concern as it can foul locks,etc.
In the scenes with the judge, there is a gavel resting on the top of his desk. Gavels have never been used in British courts.
In the scene when Sherlock is analyzing the bottom of the kidnapper's shoe, he finds traces of Glycerol/Glycerine/Propan-1,2,3-triol. The Glycerol molecule contains 3 hydroxyl groups each bonded to three carbon atoms. The show misrepresents the molecule as having 2 hydroxyl groups, and one unknown OE group, which is in fact not even a chemical compound.
When running from Scotland Yard, handcuffed, they are almost run over by a route 74 bus. Although route 74 terminates at Baker street, it doesn't display Baker Street Stn as destination but simply Baker Street.
London Buses don't have LED destination displays like on the route 74 bus, they have simple vinyl blinds.
The 2nd article to flash on the screen "Jewel Thief on Trial at Bailey" (1:18:05 remaining) repeats verbatim the 3rd paragraph/sentence as the 5th.
Sherlock jumps off the ledge onto an air bag. The bag is deflated and carried away and Sherlock also walks away. Then a corpse is thrown out of a window to make believe it was Sherlock. But, before Watson arrives, the corpse is removed and Sherlock lays on the ground with all the ¨window dressing¨.Now, why would they throw a corpse through a window only to remove it and return Sherlock to that place? Why wasn't Sherlock left here initially since Watson was out of sight.
Episode opens with Watson narrating the story to his psychiatrist, mentioning that his best friend Sherlock Holmes is dead. Story goes back 3 months to the day of Richenbach Case, followed by Jim Moriarty's crime spree, after which he get arrested. It is mentioned that his trial took 6 weeks, and story moves forward 2 months after the trial to continue Watson's adventures with Sherlock. However, by this time Sherlock should already be dead, and Watson's psychiatrist appointment must already been in past.
Everyone agrees, that Sherlock might be a creep, but of course he's very smart. So, why should he abduct 2 kids and be that stupid to volunteer to show his face to one of them in front of several policemen.