Factual error: When the possibility of Numan being sent back to Turkey arises, Carrie says "They will execute him..." The death penalty does not exist in Turkey.
Plot hole: When Brody is flown back he is wearing his uniform, complete with medals and name. But he has been missing for 8 years! Where is that uniform coming from? Not from his wife, because she just heard from him. (00:04:00 - 00:10:00)
Suggested correction: It would have been provided by the military, when he was cleaned up, debriefed and looked after immediately after his rescue. It's mentioned that he returns to the US via a base in Germany, I believe.
Continuity mistake: Just before Carrie is told Brody is going to Bluemont Park, Carrie is shown re-watching Brody's welcoming ceremony on her laptop with the speech the Vice President gave and the speech Brody gave. The footage Carrie is watching on her laptop isn't the same as when the ceremony was broadcast earlier in the episode. The footage on the laptop has the Vice President saying "Sergeant Brody, you're a man who's endured a terrible ordeal" followed by Brody walking up the podium saying "Thank you, Mr. Vice President." But what was shown earlier was the Vice President welcoming Brody home, nothing along the lines of "Sergeant Brody, you're a man who's endured a terrible ordeal." Also, the length of time Brody spent walking to the podium and saying "Thank you, Mr. Vice President" has decreased when re-watching the ceremony on the radio - the actual ceremony showed Brody walking up to the podium for about 3-4 seconds followed by a 1-2 second delay before saying "Thank you, Mr. Vice President", but re-watching it on the laptop, Brody walks up to the podium and says "Thank you, Mr. Vice President" all within a split second of replying. (00:19:40 - 00:37:40)
Clean Skin - S1-E3
Other mistake: At the river, kids are smoking pot and the guy with dark hair is telling Brody's daughter they are the perfect family. When he finishes, he is obviously rehearsing his next lines and his mouth is moving. (00:07:50)
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.
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)
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.
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 Carrie and Brody meet at the bar, his hand's position is inconsistent between shots.
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: 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: 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)
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)
Visible crew/equipment: After speaking with his son (after he has collected ice) while at the motel, Brody is facing his room door. A shadow is seen and looks to be of a person wearing a hooded top moving about, probably a member of the crew.
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.