Just two though, both regarding the irritating Major Barrymore (and not about his being an irritating martinet - not making Lt Col does take some people like that):
- WTF is this beard thing? He's in the Army not the Royal Navy (and is neither a Drum Major in a Scottish Regiment nor a Pioneer Sergeant.) That you have some people wearing scruffy beards whilst on patrol in Afghanistan is one thing but it doesn't translate to smart beards in the UK. But that's the producers not Sherlock himself.
- The medals in the picture of him and his dad. Sherlock decrees it is mid-1980s and that the father has a DSO. Complete bollocks, of course. The Dad is wearing the Conspicuous Gallantry Cross, instituted in 1993 (and not awarded until 1995), a General Service Medal with one bar and the Gulf War (1990 / 91) medal. And he doesn't have the South Atlantic Medal that the "Falklands veteran" he is declared to be would wear (this would be to the left or right of the GSM, depending on when he earned them, all campaign medals having the same precedence therefore being warn in order of award.)
I know, pointless pedantry. But given that the whole drive behind the character is pedantic attention to detail ...