Continuity mistake: Duckey is examining the two victims and taking the liver temperature. When doing this he is on one knee. Camera changes to Gibbs asking for a "T.O.D" and Duckey is stood up. (00:05:00)
Continuity mistake: When Ziva and McGee are walking up the stairs at the start, the people following them suddenly appear a lot further down the stairs. (00:02:00)
Continuity mistake: When the woman gets the baby out the car at the start she closes the car door. A few seconds later, the second woman closes the same car door. (00:00:30)
Under Covers - S3-E8
Continuity mistake: When the assassin is getting ready to take Ziva to her room, he has a jacket covering his silenced pistol. However the jacket is constantly moving in relation to the end of the silencer. (00:35:00)
Visible crew/equipment: When Gibbs walks into the bedroom at the start the film crew are reflected in the TV. (00:04:50)
Continuity mistake: At the start the girl on the webcam takes her gown off. Camera changes and now it's back on and done up. (00:00:50)
Mind Games - S3-E3
Continuity mistake: When the team are talking about Gibb's personal life, Tony's grip on his cup changes instantly. (00:12:30)
Continuity mistake: When Gibbs asks Ducky what him and Ari talks about, Ducky puts his hands on his car. Camera changes and he repeats the motion. (00:16:50)
Answer: I hadn't seen the backdoor pilots yet but while it wasn't explicitly stated, at least onscreen, I heard somewhere Vivian got either fired from NCIS due to jeopardizing a case, got resigned from the agency, or transferred to the FBI.
Raykvega423