Factual error: When Carrie is being introduced to the female Army officer, she is shown wearing a CIB (Combat Infantryman Badge). CIBs are only awarded to Army infantry and Special Forces, neither of which were open to women at the time. (00:23:25)
Character mistake: Carrie is back at CIA for a 6 pm brief. She takes a seat waiting to be called. She puts her purse under her chair. Shortly, her patience runs out and she says she is going to bathroom. She tries to enter the briefing and David escorts her out. She immediately enters the elevator and leaves. Her purse is still under the chair in the waiting room - presumably with her car keys, wallet etc.
Visible crew/equipment: When Carrie is brought back home, watch the lower part of the SUV and you can see the crew members walking. In the opposite angle, there's (obviously) no one there.
Continuity mistake: In the woods, when wounded Bassel is leaning against the tree, his collar is either wrinkled or straight, and the blood stains on it appear/disappear randomly.
Continuity mistake: When Brody is driving Nassir Faris, the trim on the passenger side dashboard sometimes has a light metal-like finish and sometimes is woodgrain. In other episodes, it's the light finish.
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.