In the opening scene, while Watson is talking to her friend, she sets her phone down on the bench after the first incoming call. When the second call comes in, a few seconds later, the phone is in her hand.
Two problems with the brief chess scene between Holmes and the morgue doctor. (1) The board was arranged incorrectly, the white corner square appears under the left side rook (should be on the right), and (2) There is a Ponziani Opening, but Holmes' opponent could not identify it after one move, it is identified after White's 3rd move.
While introducing Watson to Mr. Gertz, Holmes calls her 'doctor'. Watson has allowed her medical license to lapse, as she has stated on several occasions, and therefore should no longer be referred to by this title.