Continuity mistake: In one scene, Claire Underwood is returning to the White House from Iowa. In the hallway leading to her bedroom's stairs, she is followed by a black female Secret Service agent, obviously part of her entourage, who stops to stand guard at the beginning of the stairs. In another scene 30 minutes later, that same agent is seen standing guard at the entry of the campaigning house in which Frank Underwood is going to say his victory speech. But Claire has not flown from Washington to Iowa, so the agent should not be there.
Continuity mistake: While the first lady and secretary are playing beer pong, the secretary makes the first shot of the scene. After the first lady drinks the beer, you see two glasses in front of her and the one on the left has a ping pong ball in it already. The first lady takes her shot and misses, so the secretary goes again and makes it in the same glass we saw earlier that already had a ball in it.