Yankee White - S1-E1
Deliberate mistake: After the bad guy obtains a weapon from the armory on Air Force One, he pushes the door shut. It is heard to latch correctly, but a few seconds later when Special Agent Gibbs comes, the door is now seen to be slightly ajar. (00:38:55)
Other mistake: It would appear that (as late as early-Season 5), almost all screen shots of computer forensics include the same hard drive properties screen - it seems to be the same hard drive each time - 111GB, with 93GB used and a 129kb private container on it. I have not noticed whether they are all named drive G:, but several have been. The only thing that changes is the 'header' section, which is manipulated each episode to show something specific (but not real) for the TV audience to read.
Marine Down - S1-E9
Visible crew/equipment: In the final scene, the camera, crew and light panels are briefly captured reflected in the door of the silver sports car when Gibbs gets in. (00:43:00)
Yankee White - S1-E1
Continuity mistake: Agent Todd is standing there coat open, hands in her pockets on Air Force One watching Gibbs walk away when the bad guy who is a reporter (Leonard) comes up to her and comments "Loosening your dress code Kate". Seconds later when she turns to indicate that he should return to the press section her coat is now buttoned up. (00:33:50)
The Truth Is Out There - S1-E17
Continuity mistake: When Gibbs shows Darin Spotnitz the photo of Petty Officer Gordon and asks if he recognizes him, Gibbs' hand jumps from the top of the photograph to the side. (00:05:45)
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.
Continuity mistake: Tony boards a helicopter to go to Puerto Rico. When he lands, it's a different one. The first has the number 406 on its side.
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)
Once a Hero - S4-E8
Revealing mistake: When Ducky opens the fridge door containing the suspected killer, the dead body's eye twitches. (00:21:00)
Continuity mistake: When Tony is moving the furniture, his grip on the items is constantly changing instantly. (00:17:50)
Continuity mistake: Episode 8x21, "Dead Reflection": When Tony and Ziva are staking out PO Donner's house, Tony's grip on the hot dog in his hand changes between shots. (00:11:40)
Continuity mistake: When Gibbs is trying to talk Lt. Arnett out of jumping off the ledge, Gibbs is relatively close to Arnett in the middle of The Wall when Ducky and Abby watch the live news report, but in real time, Gibbs is over at the far left corner of The Wall. (00:04:10 - 00:05:00)
Continuity mistake: When McGee and Ziva are headed toward the sensitivity training seminar, and they notice Tony hitting on a woman at the top of the stairwell, Tony has a document in his right hand, which then jumps to his left, and then back to his right. (00:02:30)
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)
Continuity mistake: When Gibbs is on the phone with DiNizzo, Tony's phone jumps from his right hand/ear to his left between shots. (00:05:35)
Continuity mistake: When Gibbs is comparing McGee to the FBI agent's ID badge, Gibbs' left hand disappears from the bottom of the badge. (00:16:10)
Continuity mistake: When McGee shows Abby the video, the first time it starts at 0:38, and when he shows it again it starts from 0:50. (00:19:00)
Plot hole: For such a dangerous serial killer, Lt. Cobb should be more securely restrained than he is. He wears a simple pair of handcuffs, with only one security escort.
Visible crew/equipment: In one of the first episodes (2nd or 3rd) of Season 1, in an interrogation room scene, the camera pans around the table, and a crew member is visible in the far wall mirror, standing beside the camera in front of Gibbs.