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.
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.
Character mistake: When Kate pretends to be Abby, trying to trick Ari, he deduces that she's not upon seeing her gun in its holster, and doesn't pick up on the more blatantly obvious fact that her manner of dress doesn't match Ducky's description of Abby as a Goth.
Add timeCubs Fan
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.