Continuity mistake: Emily Sloane's left ring finger was shipped to Arvin Sloane in one episode in Season 2, when they are reunited in the Philippines, the left ring finger is bandaged and missing. Later, in the episode when she is shot, when she tells Arvin the CIA is listening, the left ring finger is there.
Other mistake: For secret agents, Sydney and Dixon are not very dedicated to secret identities. At several points they refer to each other by their real names in front of other people while they are under aliases. Examples include The Confession party and The Coup Las Vegas scenes.
Continuity mistake: When Sydney is tortured, she loses some teeth and a stream of blood flows out the right side of her mouth. When she returns to SD-6 and speaks with the director, the blood is gone (fair enough). Outside on the street in the following shot, the blood has returned, but there's no reason to believe that she is still bleeding.
Factual error: At the start, just after Sydney has the phone call regarding Will, she goes to meet her dad and says that they can save Will, if they get the Rambaldi document from the CIA and the ampule from SD6. In fact, it is the other way round; the CIA have the ampule, and SD6 have the page.
Continuity mistake: Season premiere, 'Authorized Personnel Only', part 1: When Sydney and the other agent are in the bathroom at the club, Sydney begins to smear black dirt on the agent's tee shirt for his punk transformation. The first smears that she applied differ when he exits the bathroom.
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Revealing mistake: In episode 3x10, Remnants, when Lazare shows up to talk to Will, we see that his left hand has been cut off. When Lazare is about to leave, he has his hands at his sides, and we can see that both arms are the same length, but the left one should be shorter, because it has no hand.
Continuity mistake: When Sloane is talking to Sydney towards the end, he slides some documents towards her. After that shot, when the shot's of Syd we can see that Sloane's holding his hands near his face, but in front shots of Sloane they're down by the desk.
Continuity mistake: When Roger Moore is showing Sloane the bank accounts, he says "5 deposits in excess of $45 million...", but the shot just before that shows deposits of (in thousands), $9,362, $7,215, $9,010, $8,300, and $9,250. That makes $43,137,000, which isn't in excess of $45 million.
Plot hole: Vaughan discovers Lauren is a mole when he goes through her briefcase and discovers the wig, gun and fake passport she used in Germany a few hours before - surely even the worst secret agent in the world would have enough sense to get rid of such incriminating evidence as soon as possible, and not carry it back to the USA (sneaking it onto a plane, presumably) and leaving it in the room where the man you're lying to sleeps. Lauren is a highly skilled agent, if the Covenant selected her for a mission this important, so it's out of character (without an explanation) for her to be so sloppy.