Continuity mistake: Tom nails the notepad with the bullseye drawing onto the tree trunk, and when he fires at the target the notepad is nailed differently and the bullseye drawing is entirely different as well. (00:27:20)
Continuity mistake: After David listens to the recording that Carrie made in order to leverage the FBI, in the closeup facing David as he says, "For what? The hope that this Imam will give you information that you don't even know he has," David's right hand is empty as he holds it up, but it cuts to the shot facing Carrie and David's hand is still up though now he's holding his pen. (00:20:15)
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.