Continuity mistake: When Holmes and Watson are arguing in the kitchen, Watson puts her mug and phone on the counter. A few times during the scene, the mug switches which side of the phone it's on. The first time it's plausible Watson moves it when off camera, but subsequent to that, we can see enough of Watson to tell she doesn't make enough movements to change the position of the mug.
Continuity mistake: Sherlock and Watson are riding in a limousine. They are seated on the back-facing seats of the limo. Thee are 2 passengers seating on the back seats. The street background visible through the back and side windows shows traffic and the limo moving forward. Some shots of Sherlock show the background traffic moving in the right direction (backwards) and one shot shows traffic moving in the opposite direction, as if Sherlock was seating on the back seat or the limo was moving In reverse.