Character mistake: Carrie tells Aayan that she can arrange for him to study at the Royal College of Physicians. The college isn't a medical school; it's a professional body.
Continuity mistake: Quinn is clean shaven when sitting by the pool with his girlfriend. The action shifts to Carrie in Pakistan and then back to DC where Dar confronts Quinn in the motel. Quinn now has a mustache and a bit of goatee, which he has for the balance of the episode. While the precise timeline is unclear, everything is fast paced and it seems that virtually no time has elapsed, certainly not enough time for Quinn to have grown a mustache.
Chosen answer: Everyone else calls him Brody or Sgt. Brody, and it probably became habit to her.
The_Iceman
Can't get the source but I read that even the Producer responded to that. Stating that it was common practise for a military wife living in a military complex as everybody refers to their husband by their last name.