Revealing mistake: After the crew transport themselves out of the book depository to escape the FBI, the astronaut helmet is transported afterwards and the two FBI agents start shooting at the box the helmet was placed on. When the box is shot, there are no bullet holes left on it.
Revealing mistake: When Lee Harvey Oswald is preparing to shoot JFK on the fifth floor of the book depository, there is a shot of him from the side where he points his gun out of the window. To his left are a numerous boxes belonging to the book depository. Many of the boxes have "books" written on them, and some have hand written numbers on them. Later in the episode, the crew go back in time to send Oswald up to the sixth floor, but in the side view shot where he points his gun out of the window this time, the boxes are completely identical to the ones used on the fifth floor. The same set was likely reused.