Brody's uniform ranking changes several times throughout season 1. At highest rank on service uniform he has the ranking of Gunnery Sergeant. In dress blues to attend dinner, he is shown with only a Sergeant ranking. In reference to repeated naming of ranking, he is referred to as Sergeant, if the Gunnery Sergeant rank is true, everyone would refer to him as Gunnery Sergeant or Gunny for short
Brody and other US Marines are referred to multiple times as "soldiers", including by a character who claims he was with a UDT (underwater demolition team, a "sister" team to the Navy SEALs who have to pass the same training). It's a point of pride among US Marines that they are marines, not soldiers. Brody refers to the UDT character as a soldier. As Naval personnel, he would be a sailor.
Marine Security Guards (MSGs) assigned to the Embassy in Pakistan do not perform bag inspections of visitors. This is done by Local Guard Forces (LGFs). Nor would MSGs be marching around the compound.
In Season 1, Raqim Faisel is shows to be a Saudi who was working as a laborer. It is very unlikely as those jobs are usually held by guest workers.
The CIA in this series does tasks that are actually the province of the FBI. The CIA doesn't arrest people, nor does it conduct surveillance and investigations of terrorists on US soil. That is entirely FBI domain. Of course, it could be part of the premise of the show the the CIA is operating outside of its authority. But if that is the case, they should at least acknowledge the legal issues. But the CIA characters openly discuss doing these things seemingly without any fear of exposure.
In a scene on-base in Kabul, a large US flag is hanging backwards. When displayed in portrait mode, the blue field should be in the viewer's upper left.
In many different episodes, Farsi / Arabic scripts are not written with correct alphabet. This usually happens when a non-Unicode software is used to write Farsi / Arabic characters.
After Brody is promoted to the rank of Gunnery Sergeant, he is constantly referred to as Sergeant Brody. He should be referred to and addressed as Gunnery Sergeant Brody, or informally as Gunny.
I don't have a problem with him showing up in his dress blues with his old sergeant stripes and pre captivity hash marks. It's reasonable to assume he didn't have time to update his dress blues.
The close personal relationship between Brody and Mike blatantly violates military regulations against fraternization between enlisted men and officers. A case this flagrant would almost certainly lead to a court-martial.
Brody prays when sun is rising. In Islam, morning prayer must be finished before sunrise, and next prayer is at high noon.
Throughout the first season, Carrie continuously calls the hijab headscarf a burka. As her character has been on service in the Middle East before, it is extremely unlikely she would confuse these terms.
In addition to showing Pakistani characters speaking Arabic, the names of the Arabs are incorrect. For example, Afzal is supposedly a Syrian terrorist, however a Syrian would be called Afdal, as the letter Dad is pronounced a hard d in Arabic while pronounced a Z in Farsi languages.
Same applies to Raqim, you would never find a Saudi of the name Raqim. And the list goes on.