Revealing mistake: Agent Lang takes a picture of a debit card inside the first victims car which is a clearly prop. The name is "Jane Doe", and the card number is 1234-5678-9101-1112. (00:05:40)
Visible crew/equipment: When Abby drops the CDs there is a yellow tape marker by one of the cases. (00:52:00)
Visible crew/equipment: When McGee asks Abby for the next batch, she turns around and a yellow tape marker is visible on the floor. (00:52:00)
Revealing mistake: When Tony takes the book off Ziva, look at the cover. It's upside down. (00:10:20)
About Face - S5-E17
Continuity mistake: When McGee is walking up the steps to the body, he is holding his camera with his left hand in one shot and then the banister in the next. (00:03:15)
In the Zone - S5-E15
Continuity mistake: McGee is looking at a report at the end and we see the page he is looking at has a few lines of text. Nothing much. Camera cuts to a close up of the report and the page is completely different. (00:38:40)
In the Zone - S5-E15
Continuity mistake: At the end, Gibbs gives Ziva a file and she takes it in one hand. Camera does an instant cut and she now has the file open in her hands and a couple of pages in. (00:38:30)
In the Zone - S5-E15
Continuity mistake: When in the square Tony's ID goes from being caught up on his jacket to hanging neatly depending on the shot. (00:16:20)
Continuity mistake: Just as Vance says about Abby being smarter than Fornell gives her credit for, he is holding his toothpick. Camera cuts and he is no longer holding it. (00:22:15)
Continuity mistake: Ziva is tasked to go outside to the FBI car and she goes upstairs passing a wooden support. Camera cuts and she passes the support again. (00:20:35)
Visible crew/equipment: At the very start, as Tony walks past Ziva, a green tape marker is visible on the floor by her. (00:00:10)
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