At the very end of the film, where Sam, Frodo and Gollum are approaching Mordor after leaving Osgiliath, it pans up over the mountains to reveal Orodruin (Mt. Doom) in the foreground to the right and Barad-Dur in the background to the left. According to Tolkien's maps, as seen in the prologue to the Fellowship of the Ring, if they were approaching Minas Morgul from Osgiliath, Orodruin would be to the left and Barad-Dur to the right. See more...
While filming the scene where Aragorn is floating unconscious down the river, Viggo Mortensen almost drowned because the rapids were worse than expected. See more...
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The entry you are changing the wording of is:
|Title||The Lord of the Rings: The Two Towers|
|Original entry||In one of the first shots of Aragorn, Legolas and Gimli, we see them running on top of a hill, with the camera sweeping over them. In that scene, Legolas' quiver is leaning on his left side and Aragorn's sword is on the wrong side. This shot is flipped.|