Continuity mistake: When the "Mole Women" are being interviewed on the "Today Show", watch the white circular table in front of them and the couch they are sitting on. The host has a small smattering of papers and a pair of glasses sitting besides him at the beginning of the scene. Throughout the scene, he will sometimes be holding the glasses and using them to gesture, sometimes not. And the papers move about from the couch, to the table, to another position on the table, etc. True, there are several shots where they are not visible, but it would make no logical sense for him to repeatedly pick up and move them between every shot where they're visible for no reason, and he is sitting in the exact same position in every shot, with his body language showing no movement towards them. They obviously shot the scene a few different times and he placed them down in different positions each time, and the scene was constructed with these different shots.
Episode #1.2 - S1-E2
Continuity mistake: When the equivalent of Miss Debenham tells the Colonel that reaching the 12 people figure might be difficult, her hands and the secretarys are in a different position compared to the previous shot (hers are raised, his are crossed in a different pattern). (00:45:45)
Continuity mistake: When Luke and the others arrive at Gateway, there's a Smart car with its doors wide open. When they start walking and the shot changes, the doors are now hardly open. The doors keep changing position depending on the shot thereafter.
Episode #1.2 - S1-E2
Continuity mistake: When Jamie and Dave are trying to drive around the old couple, you see Jamie's window is all the way down, but a few feet later when they run out of gas, we see Jamie roll his window down to talk to the couple.
Continuity mistake: Tutankhamun and Suhad ride to the Mitanni city on a horse with no equipment at all, not even a saddle. Yet mysteriously when they need to stop for the night a large tent appears out of nowhere.
Continuity mistake: Dr. Choi is playing a shootout game in his apartment dressed only in black boxers. A neighbor knocks on his door and asks him for help. Dr. Choi immediately goes to give aid, running down the hall in black pants, black sneakers and no shirt. (00:00:20 - 00:01:00)
A Rose by Any Other Name - S2-E13
Continuity mistake: During the press conference at the beginning, Hakeem has a lollipop in his mouth. During the whole scene, the lollipop keeps switching from shot to shot between being in his hand or in his mouth. (00:02:10)
Continuity mistake: When Carolyn and Ennis are racing on the beach, Carolyn in side-saddle has both her legs on the left and for just a couple of split seconds in another shot they're both on the right, and then back on the left again after that.