When Brody and Mike fight in the backyard, Brody's tie clip is disappearing and reappearing.
If you look at the three time zone digital clocks on the wall at the CIA, they list the times as "Langley - 19:20, Zulu 25:20, xxxx 29:20". Military time goes from 0000 to 2359, there is no time past 2359 hours.
Saul breaks off his polygraph, saying "we'll finish this tomorrow." In real life, that is not his call to make; polygraphs have to be scheduled at the examiner's convenience. More importantly, his abrupt termination of such a test would almost certainly result in immediate suspension of his clearance and accesses until his behavior could be investigated. That could take months, during which he would not be able even to enter the building.
The polygraph subjects face the examiner. In a real polygraph test, they are turned to the wall.
When Brody is polygraphed, he should have been asked an obvious 'NO' question as a baseline to ensure the polygraph's accuracy.
Estes is permitted to banter and add commentary to his answers during the polygraph test, which the examiner permits. In reality, the polygraph strictly requires only "yes" or "no" answers. Any additional chatter invalidates the test, forcing a do-over.
Saul's wife maintains close ties with her family in India. Saul even broaches to Estes the idea that he could serve as New Delhi Station Chief while his wife settled in the country. In reality, Saul's non-U.S. family ties would pose an ongoing issue for his CIA employment and would certainly bar him from such an assignment.
The arrest photograph for Aileen Morgan incorrectly names the local police force as "Lothian & Boarders Police", as opposed to "Lothian and Borders".
Noting that Faisel's car was spotted on I-70 west of Baltimore, Carrie assumes aloud that they'll continue through to Columbus, Ohio. No one in the room challenges her. It's a foolish and unlikely assumption for anyone who lives in the D.C. area, let alone a trained analyst. It's impossible to tell whether such a car is headed to Columbus on I-70 or to I-80 via Pittsburgh.