Gregson says the first victim had 12 pints of blood. This alone would have killed him.
As the average adult male has 10 pints and the addition of 2 more would raise the blood pressure to a fatal level.
When Sherlock is briefing the police about M, the board behind him shows a map of London (recognisable because of the path of the river Thames). It is upside down.
The football matches on TV are not Arsenal and aren't even English football.
Twice in the show M. is seen watching his favorite team (Arsenal) play matches. In both they happen at night, and given the time zone, the players would all be in bed at that time in America.
When Joan receives a text from Holmes' father is says her final check will be sent to her. No British person would ever spell it that way, it would always be 'cheque'.