Factual error: The building shown between the stated times is located in Japan instead of the US/Washington DC as suggested by the actions in the scene. This is proven by by the Chinese characters in the dark-gray concrete wall in the lower left side of the frame, as well as the red and blue colored circular road signs in the lower far right of the frame which are not in use in the US but in this combination unique to Japan. The street furniture, such as the road markings, the vegetation and the buildings also resemble Tokyo.
Continuity mistake: When Alex wakes up and goes to sit next to Tom, she puts her right arm around him so that her hand is hanging over his shoulder. In the next shot, her hand isn't visible even though his shoulder is and his hands are down. In the next shot, her hand is back on his shoulder and he's holding her hand.
Continuity mistake: When we get the shot of the President sitting and holding his glasses, the glasses change position in the next shot. When his back is to the camera, he's holding them so his thumb is in between the lenses and the earpieces are facing to his left. When he's facing the camera, the glasses are flipped over so that the earpieces are facing his right.
Factual error: When in Amsterdam, there are a number of mistakes with Hanna's car. First off, it's a brand new model, but it has a numberplate from a series six years ago. Second, that numberplate is a flat sticker, while Dutch numberplates are made with very thick plastic letters. Third, the registration is 87-UYM-3, which wouldn't be used, given that Dutch numberplates don't use vowels.
Factual error: FBI Agent Hannah Wells pulls up to the house of the First Lady's mother driving a unmarked police vehicle with government license plates. The license plate is I410918, which is a Department of Interior plated vehicle. The FBI wouldn't be driving a Department of Interior vehicle as the FBI is in the Department of Justice. A Justice plate would have a J and a FBI agent vehicle would have a regular license plate.
Continuity mistake: Emily is entering the office to pick up Tom and Aaron for the dinner, she's wearing a black dress and her hair is pinned up. In a following scene, when Emily and Aaron are talking to MacLeish, Emily is suddenly wearing a blazer and her hairstyle is completely different.