Character mistake: When Kate mentions James Bond, and DiNozzo lists the actors who have played him, he forgets Timothy Dalton. As a self-proclaimed film buff, that's not a mistake he would make.

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)
Character mistake: At the start, Kort takes the gun from one guy and uses it. He then places it at the second man's body without wiping it for prints. When he swaps his gun though, he wipes it for prints. Why didn't he wipe the first gun he used? (00:00:50)
Character mistake: When separating the bones, Ducky exclaims he has a right hand. However it is clear it's a left hand. Not a mistake Ducky would make. (00:07:00)
Character mistake: In the scene, where Jeanne tells Tony that he never said he loves her, besides after sexual activities. This is not true. In episode 15 "Friends and lovers" Tony ends a phone call saying "I love you."
Suggested correction: She is referring to the incident at the top of the climbing wall when he didn't tell her he loved her.
Character mistake: When Gibbs tells William Danforth that the body in autopsy isn't his son, he says, "Not according to AFIS." AFIS is the fingerprint database; since the body was identified using DNA, Gibbs meant to say "CODIS." (00:13:50)
Under Covers - S3-E8
Character mistake: In one scene, Jenny refers to "the former Czech Republic." That is the state's current name; it was formerly a part of Czechoslovakia.
Character mistake: In isolation, Tony mentions John Travolta and says that he's known as the "king of cool." That nickname referred to Steve McQueen, not Travolta. (00:15:10)
Broken Arrow - S8-E7
Character mistake: Ducky is a native Scotsman and refers to Dartmouth as being in "Devonshire" As any Brit would know, it's simply Devon or County Devon. (00:05:00)
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.

Lost & Found - S5-E9
Character mistake: We see McGee using his computer where the word violators is spelled violaters on the NCIS search form. (00:23:15)

In the Dark - S4-E22
Character mistake: On the message board visible in the background when the team is discussing Wong, the word "Artillery" is misspelled "Artillary". (00:18:20)

Character mistake: We see Cpl O'Neill's name on the plasma at the start. However when looking at Ducky's notes it's spelt O'Nell. Not a mistake Ducky would make. (00:03:15)
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)
Lost at Sea - S10-E4
Character mistake: During the interrogation of Petty Officer Sparks, JAG Officer Lieutenant Nora Patel says "Lieutenant Sparks has a right to legal counsel." (00:21:50)

Character mistake: We see McGee searching on his computer and the phrase "violaters will be prosecuted" is seen below the search bar. The word violators is misspelled. (00:14:50)
Character mistake: Ducky states that the Romans believed that the vein of 4th finger on the left hand ran directly to the heart, thus, logically, it was the "ring" finger. However, there is no evidence that the belief originated with the Romans, nor that the 4th finger has a special vein...the fingers in the hand have a similar vein structure.
Agent Afloat - S6-E2
Character mistake: McGee seeks Director Vance's permission to hack into the Sea Hawk's computer system. He says that in the past four months, he hasn't worked any crime scenes, etc. This is incorrect, as near the start of the episode, he and Ziva go to an officer's home to advise his wife that he is missing. They discover her murdered and then the team, including McGee, are working the crime scene.
Kill Chain - S11-E12
Character mistake: Ellie Bishop introduces herself to Delilah as Emily Bishop in the elevator scene. Her name's Eleanor in the series, but the actress' real name is Emily. She used her real first name in the scene.
Suggested correction: Ellie correctly says, "I'm Ellie Bishop," when she introduces herself to Delilah. I slowed the speed down to 0.5x to confirm.