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.
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)
Factual error: The man who approaches Carrie in the bar identifies himself as a 'lieutenant JG', and the pilot who bombed the wedding party in the farmhouse. However, it was F-15s that dropped the bombs on the farmhouse, making them US Air Force aircraft. The USAF rank structure doesn't include the 'JG' rank- that's a US Navy rank.
Factual error: The Pakistan Army uses British-style rank insignia with the crown replaced with The Star and crescent of Pakistan. The ISI officers are all wearing another badge instead of The Star and crescent. They are also wearing black gorget (collar) patches, whereas they should be wearing scarlet. Lt Col Khan and a number of other more junior officers should not be wearing gorget patches at all, as they are restricted to full colonels and above. ISI officers do not have a separate uniform; they wear ordinary military uniform if they are entitled to it.
Factual error: Throughout the season, it is the BND who run security investigations within Germany. The BND is the German external intelligence service. The internal security service, who would actually be running these investigations, is the BfV. Neither service has a power of arrest, which BND agents exercise on at least two occasions during the season. If they need to arrest somebody then they must call in the Bundespolizei (as they do correctly at other times).