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.
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.
Continuity mistake: When Gibbs comes to Abbie's lab to inquire about the smoke detector and computer, the CPU is disassembled on her lab table with the "hard drive" sitting on a white tray that is positioned in front of the computer cover that has been removed from the CPU. The "hard drive" is white colored. At the cut to a close up of the hard drive it is now black and a completely different piece, the white tray has disappeared and the hard drive is sitting on the CPU cover. When it cuts back to the wide shot the white try has returned and the hard drive is back to the original white.
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.