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: 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.
Continuity mistake: In the parking garage, after Sydney knocks the machine pistol out of the hit man's hands, it lands with the barrel pointing away from the two of them and remains in that position during their entire fight. When Sydney grabs it off the ground, the barrel is pointing toward them.
Factual error: When Sloane is talking to Emily on the telephone, Sloane's phone emits a call waiting beep and the camera focuses on the phone's screen. There are two factual errors here: 1) The phone icon for "Line 1" near the top right hand corner of the phone display is in the "on-hook" position indicating that there is no call in place. 2) The call information is displayed incorrectly. It is obvious that this is a Cisco XML card with the text entered.