Continuity mistake: When Sherlock is backstage at the circus and finds the yellow spray paint, he draws a line on the mirror. In the next shot, the line he drew is completely different (and in fact is more of a squiggle). (01:07:40)
Continuity mistake: On the video of Ian supposedly killing Alison, we see her arm fall to the ground with her "Alison" bracelet visible. But in a later scene where Emily watches Ian put his bag in the athletics room, we cut back to the video and Alison's arm suddenly has a sleeve covering up her bracelet. When we see the video again later in the series, her bracelet is visible again.
Continuity mistake: Duke is wearing an extra shirt, and his hair is longer then it was, despite continuing the scene from the end of season 2.
Episode #1.1 - S1-E1
Continuity mistake: Luther goes to see Zoe and the house is an end terrace with a red door. Later he goes back and it's mid terrace with a black door.
Suggested correction: No, I don't think this is an error. I think the house with the red door is Luther and Zoe's marital home and the house with the black door is Mark's home.
That's what I thought, but how did he know where Mark lived?
I think it's a mistake because Riply is outside keeping watch on Zoe's house. At that point, Luther didn't know who Mark was, so how could he know where he lives?
Continuity mistake: In the morning, Annie comes into the kitchen and says hi to her niece and nephew. Her jacket is alternately buttoned or unbuttoned. (00:39:30)
Continuity mistake: In the scene where Angela gives Frankie two bottles of "fruit flash", she gives him two red bottles but in the next shot you see that Frankie is holding a red and a blue bottle.
Continuity mistake: Episode 15, "FaceOff": Sophia gives Elias one hour to get the buses or else she will destroy Washington. When this happens, the sun is high, and by the time the buses arrive it is already very dark outside. (00:03:05 - 00:34:15)
Continuity mistake: In episode 3 or 4, one of the characters is knocked out and lying on the floor in the Russian sub. He is on the 'left' side of the shot most times he is shown, but occasionally he's on the right.
Episode #2.3 - S2-E3
Continuity mistake: Jack and Georgina pull into parking spot next to another vehicle. In next shot, as they walk away from their Mercedes, there is no vehicle in the next spot with no time for it to have pulled out. (00:28:15)