
Continuity mistake: We see Fornell handing Gibbs a beer at his house and his phone is in his right hand. When the shot changes, his phone is now in his left hand. (00:10:40)

Continuity mistake: When Ziva sits down to talk to the suspect in interrogation, Her hands go from clasped together to holding her one wrist between shots. (00:08:30)

Lost at Sea - S10-E4
Continuity mistake: When Gibbs pulls the empty bottles out of the evidence box, he pulls three out and places them on the desk. However, when the camera changes to behind Gibbs, there are only two bottles on the desk. (00:24:10)

Lost at Sea - S10-E4
Continuity mistake: The way Gibbs holds the key card that Ducky gives him changes between shots. Watch the sides of the card. (00:09:30)

Visible crew/equipment: When Tony approaches the woman on the shooting-range, a white rectangular screen can be seen reflected in the glasses she is wearing. (00:22:10)

Continuity mistake: When Tony is looking at the flight plans to Malta, The way he holds the paper changes. Note the glove and his grip. (00:05:10)

Visible crew/equipment: At the naval yard when Ducky is exiting the cab, as it drives off you can see an orange tape marker on the floor. (00:24:30)

Lost at Sea - S10-E4
Continuity mistake: When Borin and Dinozzo are talking about why she accepted the date, Borin's hair is constantly switching/moving place. This is not because of the wind. (00:27:00)

Lost at Sea - S10-E4
Continuity mistake: When DiNozzo says about the bet being off, his facial expression changes completely in an instant cut. He goes from concentrating and serious to joking and laughing. (00:27:30)

Continuity mistake: When we see Ducky arriving back at the naval yard, two men walk past his cab but when the shot changes, they walk past again. (00:24:20)

Continuity mistake: When Ziva is on Tony's shoulders, she goes from grimacing and looking at the floor to looking above her and not grimacing as much instantly. (00:04:00)
You Better Watch Out - S10-E10
Other mistake: McGee's text to Tony says "Dell's body found. Rock Creek Park." The suspect they are looking for and body found is named Justin Cannady. (00:22:23)
Visible crew/equipment: While at Gitmo, Sergeant Spooner is attacked by a detainee, and when Tony joins in the tussle the gun is fired. It then cuts to the tented Global Courier van, and the pink tape mark is visible on the ground behind the van. (00:35:50)
Factual error: There is a flashback scene in this episode, where a young, dejected Abby Sciuto is walking along railroad tracks after failing to give the bear back to Ricki. This scene starts with a shot of the railroad tracks, then pans up to Abby. It can be seen that the rails are laid on concrete sleepers, with modern steel clips holding the rails to the sleepers. Given that the flashback appears to take place when she was at least a couple of decades younger (i.e. the mid-1990s), such modern methods of construction wouldn't have been used. A period-accurate railroad track would have wooden sleepers, spikes and lighter rail. As such, it's obvious that the producers just went to the nearest railroad tracks and filmed the scene there.
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)
You Better Watch Out - S10-E10
Continuity mistake: When Tony's dad arrives at the NCIS office for Christmas, he is met at the elevator by Ziva. He is holding a Christmas present (which looks like a bouquet of flowers) with the 'red' end up. As the camera angle changes, he is now holding it 'red' side down. (00:28:25)
Chosen answer: It is never stated, however she must have been there several years if she is on presidential detail.