Continuity mistake: Carrie Matheson leaves her sister's house in a Jeep Compass with her daughter. When she arrives at her destination, she is in a newer model of the Jeep Compass (the front indicators are different).
Continuity mistake: When Sgt Brody first returns to the US, he's seen in uniform wearing a sergeant's three chevrons with one hash mark, indicating at least 4 years of service. Later, he's a Gunnery Sergeant, with two rockers below the chevrons, plus two additional hash marks to reflect the eight years he was a POW. In the episode "Achilles Heel," Brody and his wife attend a swank Capitol Hill party, but his dress blues have only the three stripes and single hash mark. Throughout the series, everyone addresses Brody as "Sergeant" and never as "Gunny," which is the traditional reference for a Gunnery Sergeant. (00:22:00 - 00:28:00)
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.
Continuity mistake: Shortly after halfway through the episode, Carrie Matthews discusses the fate of her unborn child with her sister and father. Her hair is not tucked behind her ears - then it quickly is.
Continuity mistake: Saul, Dar and Lockhardt leave Saul's office and walk through an open door into the adjacent conference room. The connecting door remains open but in the next shot the door is now closed, enabling Saul to lock the senator in the conference room.
Continuity mistake: When Saul is at the terrorists' house talking to a neighbour, his arms are either falling down straight or bent, depending on if it is a front or a back shot.
Continuity mistake: When Brody is captured in the previous episode his head is completely shaved. This episode takes place no more than a few days later (it is actually implied that it is three days), but he now has a full head of hair.
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.
Clean Skin - S1-E3
Continuity mistake: When Jessica and Dana are in line for the Gaucho Taco drive-in, Jessica has one hand on the wheel, yet a frame later, from a different angle both are on the wheel.
Continuity mistake: SPOILER - When Brody and Carrie are in the car having sex with her laying down, the shots behind her head show a big amount of space in-between her head and the door, yet the front shots show it squashed against the door.
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.
Continuity mistake: When Carrie is talking to Brody from across the room, her hair jumps several times between being tucked behind her ear to hanging down by her face. (00:20:30)
Continuity mistake: Carrie opens the safe to take out her gun. The safe is closed when they take her with a hood. When Quin comes in the safe is open again.
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)
Continuity mistake: When Lt Col Khan leans forward in the airport scene his epaulette can be seen to bear only the single pip of a second lieutenant. When he stands up again he is wearing the pip and emblem of a lieutenant-colonel once more.
Continuity mistake: As the young girl is in the kitchen cooking and goes to answer the door she puts her sari on. When she answers the door it's no longer on her head and is around her neck. When she closes the door she then has the sari back on. (00:05:10)
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.