Continuity mistake: When Carrie waits to "accidentally" bump into Brody outside the CIA building, watch the extras really making a mess of the continuity.
Visible crew/equipment: When Mike comes home after Jessica's call, he steps out of the car and film crew and equipment are reflected on the side of his car.
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.