Other mistake: The body had multiple stab wounds on its back, but there was hardly any blood on the clothing. Even if the body was moved post-mortem, the clothing should have been saturated.
Plot hole: We see Gibbs fire his sniper rifle and kill Saleem from a hill several hundred meters away over hilly and sandy terrain. We then see him shoot a guard while Tony and McGee are getting free. By the time they have walked down the corridor (about a minute) Gibbs has appeared in the hallway in full desert sniper suit. (00:40:00)
Continuity mistake: 7.05 - Code of Conduct. Gibbs and Tony go to question a marine who is exercising. The sweat stains on his shirt get much bigger and smaller, as well as change shapes, throughout the interview. (00:20:35)
Factual error: The commercial 747 landing in Washington from France is the president's plane Air Force One, not a regular passenger jet. It's actually reused footage from the film Air Force One.
Jack Knife - S7-E15
Visible crew/equipment: When Ziva and Damon walk to the back of the truck, the trailer doors are opened to reveal cases of watermelons, and just as Ziva says, "Melons," the red tape mark is visible on the ground between her feet. (00:25:20)
Visible crew/equipment: When Vance and Gibbs are in MTAC discussing the Damocles and Ziva, Vance decides on doing the good cop bad cop, and in the next shot the tape mark is visible on the floor, as Vance and Gibbs head out. (00:05:30)
Visible crew/equipment: When McGee tells Abby to show him what she's got, as they walk through the doorway the reflections of crew members are visible on the glass. (00:25:30)
Visible crew/equipment: When Tony opens the car door at police impound, McGee enters the car then starts to do his thing, and the camera's reflection is visible on the passenger window. (00:31:00)
Visible crew/equipment: When interviewing the DEA agent, there is a green reflection and a tripod stand reflected in her glasses. (00:11:40)
Visible crew/equipment: When Gibbs and MaGee are reviewing Parsons' military record, the boom mic is reflected in the TV screen.
Borderland - S7-E22
Continuity mistake: At the crime scene, McGee has his notepad lowered. Camera changes and now he's writing on it. (00:04:50)
Borderland - S7-E22
Visible crew/equipment: When the kid asks if crushing a car hurts, you can see the film crew reflected in his glasses. (00:00:55)
Continuity mistake: McGee asks Tony to take his foot to the locker room. When he does Tony is holding the red towel between his toes. Camera changes and now he's holding his foot. (00:02:47)
Continuity mistake: When Gibbs throws the van keys they land next to a desk. When Ziva, Tony and McGee all scramble for the keys, they are in the middle of the floor. (00:03:20)
Continuity mistake: When Igor is cuffed at the end, his coat is hanging off one shoulder. Camera changes and now it's back in place. (00:39:50)
Jack Knife - S7-E15
Continuity mistake: When Szwed walks past his trailer, he is in the middle of the liveries on the trailer. Camera cuts and he's jumped about 6ft. (00:24:00)
Jack Knife - S7-E15
Continuity mistake: In the surveillance van, McGee has 2 cups of coffee. He grabs the one nearest Tony. Camera cuts and now he's taking the lid off the other cup. (00:20:50)
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