Factual error: When Faramir and his men are looking at the map of Middle-Earth in Henneth Annûn, you can see that the plain of Dagorlad is actually spelled Dagorland on the map. An odd mistake, especially considering the fact that they got it right when they spoke of it in the first movie.
Factual error: 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 The Tower of 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.
Factual error: When the refugees from Edoras are on the move to Helm's Deep, against the mountain range backdrop, they are going the wrong direction for a mountain range viewed from the north, where Rohan and camera are presumed to be. They should go from left (east) from Edoras to right (west) to Helm's Deep, but instead we see them going right to left, i.e. west to east. This occurs in two long-range wide-field shots.