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.
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)
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.