Revealing mistake: 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.
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.
Continuity mistake: When Sydney is torching the lab you see 6 test tubes labelled with her name shatter and spill. In the next shot the tubes are back on the rack and intact. (00:38:20)
Other mistake: When Jack logs into Lauren's e-mail account, for one, the birth dates on Lauren's IDs say 1959 and 69 (which would make her either 33 or 44). Plus you can see (possibly) real e-mails from actual crewmembers, for example at the bottom you can see "FW:Photos for Alias Ep.#315." (00:10:57)
Continuity mistake: At the beginning of the episode Sydney has a fringe. In the next scene she's shown with no fringe.
Chosen answer: It does sound overdubbed, but there was no change in the organization. UCO is United Commission Organization. There are signs when Patel is coming that say UCO so obviously it wasn't changed.