Character mistake: When Gibbs shows Major Dorden his badge, his ID card is upside down. (00:06:00)
The Truth Is Out There - S1-E17
Character mistake: Gibbs and Ducky are in Autopsy, with Ducky describing lower-leg injuries of a deceased Petty Officer. The two bones in the lower leg are the tibia and the fibula; however, Ducky, a doctor with decades of experience, referred to the injuries as fractures of the "tibia" and "fibia." (00:13:05)
Yankee White - S1-E1
Character mistake: The uniform/costume that Major Tim Kerry, a Marine Military Aide to the President, is wearing, includes a Service Aiguillette made of 4 loops of round gold wire and scarlet cord. This aiguillette is worn by a Marine serving as an Aide or in other positions for a 4 Star General. A military aide to the President would wear 4 loops, all gold (as seen being worn by Commander Ray Trapp). (00:29:00)
Character mistake: When Gibbs first looks at the victim's body and sees his rank, he incorrectly refers to him as a Lieutenant when the rank is for a Captain.
Bete Noire - S1-E16
Character mistake: Ari tells Ducky and Gerald that if they lie or he suspects them of lying, he will shoot them in a ball-and-socket joint. Ari later shoots Gerald in the shoulder and mentions that next time it would be his knee. The knee is not a ball-and-socket joint. It is a hinge joint. The only other ball-and-socket joint in the human body is located in the hip. Ari is an educated Doctor and should know the difference. (00:24:00)
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