Continuity mistake: Agent Wells is chasing the bad guy on foot. In the first shot her SIG is not cocked. In the next shot it is cocked. In the next shot the slide is retracted. In the next shot she somehow magically fires it. Then the hammer is somehow forward again. A few seconds later as she climbs the stairs it supernaturally transforms into a Glock. And at no time does she use a proper grip on the gun.
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. (00:06:55)
Other mistake: When Agent Wells tells the White House they need to alert the Pentagon that Lozano is inside the Pentagon, she is told "it's already done, they are locking down the building right now." Then, later in the same episode, we see Lozano use a key card to easily pass through the building. (00:15:45 - 00:21:15)
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.
Continuity mistake: Agent Wells spots Lozano leaving the Pentagon and begins a high speed chase. During that chase Lozano is alternately wearing and not wearing his seat belt. In addition, Lozano's car is only damaged in the close-up scenes; whenever the car is shown from a distance, it is completely undamaged, even after Wells has rammed him repeatedly.
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.
Continuity mistake: When Hannah Wells and Jason Atwood confront Brooke Mathison and she tries to fight back with her hidden pistol, Jason fires three shots at her, while Hannah fires two shots at her. However when they show Brooke Mathison again, only one shot is visible on her body. Because she was facing Jason, there should have been at least the three shots he fired at her visible. (00:39:53)