Continuity mistake: When Eytukan orders Jake and Grace to be tied up, Tsu'tey and another Na'vi grab Jake and bind his wrists, his right on top. It switches to Eytukan shouting a war cry, and goes back to Jake; his left wrist is now on top.
Continuity mistake: When Jake's avatar is running through the garden as he first enjoys having working legs again, he skids to a stop on the loose topsoil in the aisle of the garden. The next shot that shows him wriggling his toes in the soil reveals a pristine path of soil and no evidence of the disturbance his skidding to a stop caused.
Continuity mistake: There is a scene where Jake and Grace are tied up by the natives, shortly after they are cut down, Jake pushes Grace over a log to avoid an explosion, the shot changes to something else, then returning to the log, and we see that he's pushing her again. then the shot continues.
Continuity mistake: In the colonel's robot there is a rear-view mirror. When we see the robot from the outside, it is very close to his head. But when we see shots from inside the robot, there is plenty of room around his head and we don't see the mirror.
Continuity mistake: When Jake tames Toruk, he confronts the Na'vi and speaks to Tsutey. While Jake is speaking to Tsutey, Tsutey's braids are over his shoulder. After Jake says "You are Oloektan," all but a single braid are behind his shoulder. After this, when Tsutey looks at the Toruk in the distance, a braid or two fall over his shoulder, in the next cut no braids are over his shoulder.
Continuity mistake: When Sigourney Weaver is shot in the stomach, she is not wearing make-up. When she is transported to the Tree of Life and laid under it for possible rejuvenation, she is wearing mascara.
Continuity mistake: When Jake is learning to ride on the direhorse, after he is corrected when calling she a he, and is hit on the head by the direhorse's queue, his braid slips over his right shoulder, but next shot the braid has returned to his back.
Chosen answer: The Core didn't originate the name - it's been used since the 50's and even has its own Wikipedia article at http://en.wikipedia.org/wiki/Unobtainium. There it's described as "any fictional, extremely rare, costly, or impossible material, or (less commonly) device needed to fulfill a given design for a given application."
Jon Sandys ★