Factual error: Raceme's girlfriend Morgan is seen in a mugshot taken by Edinburgh Police, Scotland. They are known as Lothian and Borders Police, not as shown "Lothan and Boarders". (00:28:30)
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).
Factual error: The Pakistan Air Force officer in the airport is listed in the credits as 'PAF Lieutenant' and is wearing the two pips of an army lieutenant. In fact, the PAF still uses RAF-style ranks, so he should be a Flying Officer, and the PAF also uses distinctive eight-pointed stars instead of pips.
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)
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.
Factual error: Before Jonas discovers Quinn is gone, he calls the emergency number, which is 112. However, the lady on the phone says "zwei eins eins" (211).
Other mistake: When Carrie leaves through the tunnel to the street, when she comes out of the store there's a shot of 2 people kinda looking at her. That shot was horizontally flipped - look at the sign on the door. (00:34:05)
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.
Casus Belli - S6-E5
Plot hole: Later in the evening, after NYPD takes Quinn into custody, Carrie finds his cell phone, with pictures showing their home had been spied upon from across the street, as well as other evidence of a conspiracy. He had tried to hand her the phone right after the police broke in, but it was knocked from his hand and she discovered it under the smashed door. In the real world, Carrie's home would have been considered a crime scene and the police would have searched it thoroughly, top to bottom, undoubtedly finding the phone themselves, but are shown driving away after the confrontation.
Factual error: The President's casket is being brought into hanger at Dover AFB Delaware. There are no mountains in Delaware as was seen in the background.
Factual error: Almost anytime where an ipv4 address is shown it contains one or more digit exceeding 255, impossible given the limits of the technology. eg: 257.100.23.59, 23.274 .44.67, and even 316.105.147.373. (00:04:55)
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.
Visible crew/equipment: When Brody and Carrie exit the bar and open the car door, a big lighting equipment screen is reflected on the door.
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.
Super Powers - S5-E3
Factual error: Carrie loads a rifle with at least a 7mm Remington, possibly a .30-06 Springfield bullet. She shoots Quinn in the back one time, and he falls, only to disappear and reappear where he chokes Carrie from behind. He later removes his jacket to reveal he's wearing a soft armour bullet proof vest. The armour he wore was maximum level 3A vest which will only stop handgun threats. He would require a plate carrier with SAPI/ESAPI ceramic plates to stop such a threat. (00:55:37 - 00:57:10)
Factual error: As Brody is driven away from the square after meeting Abu Nazir's widow, the shot from inside his car reveals a public telephone box on the corner. He is supposed to be in Tehran, Iran - however the distinctive colours of the phone box are those of Morocco (where I assume the scene was shot). (00:35:40)
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.
Visible crew/equipment: While Carrie is questioning the Saudi diplomat, the camera crew can be seen in the reflection of the diplomat's glasses throughout the scene. (00:27:00)
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.