Other mistake: When you are in Isengard in the Hub World, notice the grey stands around the place. You will notice there are no wood planks in part of the stands. But if you stand on top of the empty space, it is clear you aren't falling through, but just standing on top of an empty space.Casual Person
Other mistake: King Theoden's aide with long orange hair announces that the King ordered that everyone make refuge for Helm's Deep. However, the king has just come out of Wormtongue's curse, and had only talked to Eowyn and Gandalf, so he couldn't have told the aide.
Other mistake: During the Witch-King boss fight, there is a carcass of a dead Mumak to the left. But if you go far enough to the left, you can see that the saddle is just floating there, without a Mumak carcass.