When Gibbs is outside Director Shepard's townhouse, he's leaning on the front end bumper of his car. When he calls her, the car's headlights are on. When she looks out the window, they are off.
When Ari and Ducky drive off in the Morgan it makes the sound of a V8 yet it's a 4/4 meaning 4 wheels and 4 cylinder the body is too narrow for a V8.
When Tony offers Ziva the pizza slice she takes it in the middle in the next shot she's taking it by the crust.
At Kate's funeral her casket is draped with a US Flag. During the funeral, the flag should be removed, folded into the triangle, and presented to family or a designated person, but as the funeral ended, the casket is still draped with the flag with flowers placed on the flag. Nothing is ever placed on top of a flag covering a casket.
Gerald's and Ducky's phones do not have GPS built in so they wouldn't be able to get a trace.
The Presidential Medal of Freedom around Kate's neck when Gibbs "sees" her in her casket at the cemetery is on the wrong ribbon.
When Tony and Ziva are talking outside the hotel, he says "Buena Notte," telling her good night. However, in Italian good is "buono" not "buena". The proper salutation would be "buona notte" or "buona sera".
In the good night exchange between Tony and Ziva, where Tony screws up the Italian salutation, Ziva does likewise with Hebrew. Ziva says "laylah tov" (long A sound) instead of "lailah tov" (short A sound).
As Special Agent McGee goes down to look at Agent Caitlin Todd's body in the autopsy room, we can see that there is no bullet wound on her forehead even though she was shot there. If you look closely however, you can see a different skin tone where the bullet hole was but has since been covered over by Dr Mallard prior to the funeral.
Director Shephard makes an announcement that Cate's funeral will be the next day in Indiana however McGee visits her body later in the morgue. If the funeral were the following day then Cate's body would have already been transported to Indiana.
Ducky must have been Americanised as he called a phone a cell phone as a British person he should say mobile phone.
When McGee is placing the flower on Kate's casket, he has a flashback of her climbing up the roof from the first episode of the second season. However it is an angle he couldn't have seen her from because she was standing on his shoulders just prior to her climbing up that roof.
As DiNozzo is conducting surveillance on Ziva outside the hotel in the rain, Ziva comes out; there is a box of pizza and Tony is about to pitch it out and she tells him there is a piece still in the box. He takes it out and hands it to her. You see that there is pepperoni on it. Even Israeli secular Jews keep kosher for the most part. You see her take a nibble from it.
Gibbs uses 'Julia' as the phonetic for the letter J when it should be 'Juliet'.
According to Jewish law, religion follows the mother. Ziva would not consider Ari Jewish and wouldn't say (quietly to self at end) the Jewish funeral prayer on him.