At the end of the show Holmes and Watson are watching a Mets-Reds baseball game on TV. This would be impossible since this story takes place sometime during the winter, as everyone is wearing heavy winter clothes and all of the trees are bare.
When Sherlock Holmes and Dr. Watson approach the initial crime scene, Sherlock's scarf, gray on one side and red on the other, had the gray side out and the red side against his skin. When we see them inside the brownstone, the scarf is showing only the red sided pattern.
When Sherlock and Watson get off the train, Watson's iPhone receives a call from Mom & Dad and clearly we see the options for "Answer" and "Decline", which would happen only if the iPhone was not screen locked, but after Watson selects "Decline", we hear the distinctive "keypad lock sound" of the iPhone, which would never happen unless the iPhone was screen-locked when the call is received.