Continuity mistake: The underground car seen in the CCTV video is from the Jubilee line, but is meant to be the District Line. It's also different from the one where the heroes defuse the bomb, which is an actual District Line train (D stock). The rounded doors is the most visible proof.
Factual error: Sherlock takes pains to explain in detail that he will deliberately corrupt the magnetic code stripe on an access control card he intends to use to enter the elevator to the villain's penthouse, by carrying it next to an operational cell phone. (This is possible due to the low frequency magnetic field from a phone's vibration motor.) But when he actually goes to access the elevator, he simply touches his access card to the reader instead of swiping or inserting the card through a slot, which is how a magnetic stripe reader would operate. The elevator uses an RFID proximity reader, not a magnetic stripe reader - a phone wouldn't corrupt an embedded RFID tag.Stringman
Character mistake: While the original Sherlock Holmes is famous for making water-tight deductions, the one in this episode does not quite live up to that standard. He declares someone a "compulsive cheat," because: "Waterproof cover on his smartphone. Yet his complexion doesn't indicate outdoor work. It suggests he's in the habit of taking his phone into the shower with him, which means he often receives texts and emails he'd rather went unseen." There are far too many problems here. (1) The only type of complexion that indicates outdoor work is sunburned. We don't have water-soaked or snow-frozen complexions. So, yes, he might work outdoors. (2) Indoor work may also deal with water, e.g. plumbing, dish washing (note what the accused man is doing!), water purification, lab work, etc. (3) Some people might just purchase a waterproof cover as a precaution. Some might receive it as a gift. Some may receive it free during a bulk purchase. (4) Not everyone who takes his or her phone into the shower has fidelity problems. They might want to listen to music, be up-to-date with the stock market, or, if I may use a euphemism, might want to have some quality alone time. (00:12:35)FleetCommand
Continuity mistake: The train carriage that disappears is a Jubilee line carriage. These trains have the bars inside them painted bright yellow. However, later on in the episode when Sherlock discovers the disappeared carriage, it has magically turned into a District line carriage (the bars inside are bright green).swordfish
Continuity mistake: As Sherlock and John approach the missing subway car, and especially as they bend to peer beneath it, the interior of the car to a distance of several feet is plainly visible through the window of the door (you can see the curved ceiling inside and some unlit fluorescent light bars). However, an interior shot then shows that there is a closed door inside the car, a foot or so inside the exterior door, that Sherlock has to push open to enter the car proper. This door should have blocked their view of the inside of the car before they entered. It didn't, so it has gone from open to closed between shots without anyone touching it. (01:05:35)Aerinah
Plot hole: Sherlock manages to convince Janine to let him into Magnussen's quarters after deceiving her into thinking he is going to propose. Several days later, she is enjoying her "revenge with profits" on Sherlock for his duplicity. Problem: There is no way she could have found out. She was out cold moments after letting Sherlock in, and Sherlock himself was shot by an assailant, which he had misidentified. Only Watson knew Sherlock's true intention, but we know he did not reveal it. The shooter and Magnussen did not know and had no opportunity to tell Janine anyway. (Plus, Magnussen's credibility is too low.) In fact, if I were the director, I wouldn't bother making up a motive for being a "grasping, opportunistic, publicity-hungry, tabloid whore" (film's own quote). Such a person loves "profits", not just "revenge with profits." (00:31:00 - 00:43:00)FleetCommand
Factual error: The entire reason Sherlock takes up the case is because he is intrigued how a man managed to disappear from a tube carriage in between stations - it appears to be impossible to do. However, any Londoner will tell you that it is perfectly simple to do: all tube carriages have doors between them linking them. So if the man wanted to leave the carriage between stations, he'd just use the door at the end of the carriage. The train employee would not be puzzled by this, nor would Sherlock consider the case worthy of his time.swordfish