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.
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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.