Marine Down - S1-E9
Continuity mistake: When Gibbs tapes Kate's palm pilot to the target it hangs vertically. Camera changes and now it is hanging horizontally. (00:03:15)
Visible crew/equipment: When Dr. Mallard is talking to Mr. Palmer about a "White Elephant", you can briefly see crew members on the stainless steel door on the left of the screen. They are blurry, but distinguishable. (00:23:55)
Continuity mistake: When DiNozzo rings Gibbs, we can see Kate taking metal scrapings on a pole that has tape on it just above her hands. When we get a closeup of Kate, the tape is not there. (00:25:50)
Continuity mistake: When the lady at the base exchange is throwing stuff at Tony, Tony has a yellow shirt in his hands that disappears, only to be thrown again. (00:24:00)
Continuity mistake: At the end the little boy tells Gibbs the password he has chosen for his tree house. As he does, Gibbs is working on the railing at the opposite end to the ladder. Gibbs says it's a good password and to come up. However he is now at the end of the railing by the ladder. (00:39:50)
Continuity mistake: At the very end we see Gibbs working on the treehouse. As the little boy climbs the ladder, Gibbs is working on a railing. Camera changes and now he is stepped back from the railing. (00:42:00)
Continuity mistake: When DiNozzo is reading the ingredients of the brass stripper, he has 2 hands on the tin in one shot and just 1 hand in the next. (00:29:00)
Yankee White - S1-E1
Continuity mistake: When Caitlin leaves the Cafe, Tim holds the car door open for her and she gets in. He then closes the door and leans on it. Camera cuts to a different angle and now he is stood up straight and slightly back from the car, with no time to do so. (00:29:05)
Yankee White - S1-E1
Continuity mistake: Just after Gibbs lies down on the slab, we see a shot of Ducky smirking. In this shot, we see Gibbs in the background turn on to his side. Camera changes to Gibbs and he is on his back and then turns onto his side. (00:24:00)
Yankee White - S1-E1
Visible crew/equipment: When Ducky tells Gibbs to go home and get some sleep, Gibbs walks over to the side and grabs some paper towels. When he does, the camera crew is reflected in the fridges opposite. (00:24:00)
Rendezvous - S14-E24
Revealing mistake: While McGee is bandaging what's left of Dean's arm you can see the arm is way to long to have the hand missing, you can tell the actor's hand is still there.
Continuity mistake: When Gibbs drops the nails on the food carton, the position of the nails goes from spread out to grouped together instantly. (00:19:50)
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