Whoops.. Lost My Sword
In the scene where Aragorn, Legolas and Gimli meet Eomer for the first time, look closley at Eomer after he gives them the two horses. When he says, "Look for your friends, but do not trust to hope," look at his sheath, near the bottom of the screen. You can see that his sword is dangling out of its sheath, and then falls out. (This is hard to spot, you may need to do frame by frame)
Reverse Footage Used
When the Ents attack Isengard, look closley at Saruman at the balcony. In one of his shots, his hair is blowing backwards AKA reversed footage.
During the battle of the Deeping wall at Helms Deep, you can see one elf at the left of the screen aiming and firing his bow, complete with sound effect. The problem? There is no arrow notched.
Change of Clothes
During Sam's "The stories that really mattered" speach near the end of the movie, Aragorn changes his clothes twice. After Theoden shouts, "Victory! We have Victory!" Aragorn shows up wearing his Helms Deep battle clothes. then he walks up to Eowyn wearing the clothes he fell into the river with while fighting the wargs. Then when Gandalf leads everybody up onto a ridge, Aragorn is wearing his Helms deep clothes again.
Shadowfax has a Saddle
Throughout the entire move, Shadowfax has no saddle for Gandalf to ride on. If you look closly at the end of the move when Gandalf rides to the top of a ridge, you can see that Gandalfs feet are in stirrups. Guess he didint feel safe about charging down the hill withought a saddle.
How Did That Get There?
At Osgiliath, one of Faramir's men is carrying Frodo and Sam's swords at all times. So how did Frodo get Sting back to try and stab Sam?