Lowe's costume is that of a Corporal, despite being called Major.
Despite holding the rank Lieutenant General, Lieutenant General Civil wears the rank of a Major.
Lowe is wearing both his medal ribbons and full medals during the meeting - he would have worn one or the other, not both.
The Prime-Minister's Family is called the "First Family" this term is only used in America, not in the UK.
The film depicts 10 downing street being under seige and it made it look like it would be easy to do clearly not as it would have been done in real life the downing street set is wrong and probably isn't british made downing street under seige there would be scotland yard mi6 all over it.
Lowe's salute is very dissimilar from a British Army salute, and is closer to that used by the U.S. military.
The correct way to salute in the British armed forces is described in detail in 'www.forces.net/technology/uniform/how-official-guide-saluting-military'. The correct army salute is with palm facing forward. As such this categorically is not an army salute.
It is possible that as the SAS take a significant number from the Royal Marines (part of the navy), that such members may be entitled to retain their navy salute (palm facing downwards - as performed by Lowe).
The salute performed by Lowe, however, is not that of the navy as such a salute brings the arm upwards in front of the body and not out to the side.
Lowe's salute was categorically not that of a member of the British armed forces.
A view from the Roof of Downing Street is completely wrong and shows suburban homes and hills, rather than what should be Whitehall.
Downing Street itself is also completely wrong with buildings shown at the end of the Street and a columned House where Number Eleven Downing Street should be.
Lowe mispronounces Lieutenant as in British English it is pronounced "Leftenant". He pronounces it in the American English way. This would be unacceptable for military personnel such as himself.