Once Abby cracks the password and filters the Element song, she starts writing Atomic Numbers on a sheet of paper. When she gets to the bullpen, the numbers are written differently.
When they are walking past the NCIS 'Most Wanted' they pass Roland Alan Moore who has not been crossed off. It was clear Gibbs and Agent Reyes arrested him in 'Terminal Leave'.
When Jill Reynolds walks into the room where her husband sitting dead at the computer, the spear is not visible in his back. When Stephanie walks around to say hello to him, suddenly the spear is sticking out of his back and should have been visible over the back of his chair.
(at around 52 mins) Abby says "It could be hidden in a secret partition of RAM" after thinking about checking the laptop rather than its disk image for the password. RAM memory in modern computers is seldom partitioned at all, but consists of a constant pool. Also RAM memory is volatile (it loses data when powered off) and the laptop had presumably been turned off for several hours at that point. Although it is possible to recover pieces of data from RAM memory after considerable time without power, Abby would have had a hell of a day figuring out which pieces are relevant, how they are coded, and what has already evaporated.
Abby says there are no simple classes of atomic substance will keep her from her appointed duties. In fact there are several classes of simple atomic substances that would keep Abby from her appointed duties. Depending on how she is exposed several of the heavy metals (such as arsenic or lead) or radioactive substance (such as Uranium or plutonium) would make Abby very ill or even dead. They would be very effective in keeping Abby from her appointed duties.
Col. Mann is understandably angry that Gibbs concealed information about his fourth marriage (and the death of his first wife and daughter) from her when she learns of this fact from Ducky. In the episode Sandblast when Gibbs and Col. Mann first met Col Mann did make one reference to Gibbs having four marriages, however there was no way for her to know of more than his three divorces, and that is accepted to be a scripting mistake.
The screen display indicating that the hard drive data is unrecoverable says "NO RECOMENDATIONS" rather than the correct "NO RECOMMENDATIONS".
At approximately 6 minutes in, when the characters are in the director's office, a light shield can be seen at the bottom of the screen as the camera pans to the left.