When Carrie is studying with Virgil, the cards he holds change colors.
Prepping for her encounter with the Saudi diplomat, Carrie recites his children's names, including a "Gamilah." That's the Egyptian pronunciation. In Saudi Arabic, as in standard Arabic, the name is Jamilah ("beautiful"). Considering her field of expertise, Carrie would know that. If anything, she would mispronounce an Egyptian girl's name as "Jamilah."
In some scenes, Brody is wearing the rank of sergeant. In others, he is wearing the rank of gunnery sergeant.
Jessica is shown bringing home groceries in bags printed with "www.hemarket.com". This is a chain of stores exclusively in the Charlotte area where the show is filmed, with no stores anywhere close to the DC metro area where the show takes place.
"Farragut Square" is spacious, landscaped, and upscale with a fountain, stream and bridge. The real Farragut Square is small, dominated by a statue, hemmed in by buildings and has no running water of any description.
Brody runs for Congress while on active military duty, even appearing for the announcement of his candidacy in full military uniform. This would be a gross and highly public violation of the military code of conduct and would destroy both his military and political careers in one blow.
While staking out Farrgut Square, Carrie responds to Saul's cautions by saying into her microphone, "I know the protocol. This isn't my first polka." At the instant her words are being said, she is pacing in the open and looking around in an extremely conspicuous manner.