Other mistake: During the denouement, there is a scene with the meeting between Simon and Jacqueline inside the doctor's cabin. Jackie opens the doctor's case where he keeps the surgical tools pulling it out from a drawer, and she does not place the box back in the drawer or closes it; we see the whole time she spends inside the cabin, so it'd be impossible for the doctor not to notice what happened. (02:08:25)
Other mistake: When the Fellowship takes a rest after escaping the snowstorm, Gandalf and Aragorn begin arguing about which path to take from there. When Aragorn suggests the Gap of Rohan, Gandalf protests, saying, "That will take the Ring too close to Isengard," followed by "and Aruman" instead of "Saruman." (00:55:00)
Other mistake: The opening credits list Tomas Milian, Bo Svenson, Gille Kirsten, etc. Everyone (before and after) by FirstName LastName as customary, except Kirsten Gille.