Other mistake: At the battle of Helm's Deep, Theoden, Aragorn, Legolas and the rest ride out of the Keep to meet the enemy, watch as the first men out of the gate kill all the Uruks on the bridge, yet the men riding behind them continue to hack and slash away at thin air. (02:38:30)
Suggested correction: Not quite a mistake. These men most likely slashed at the air in order to scare the Orcs away or protect themselves from other kinds of danger, like Orc arrows. I saw a few movies where knights slashed their swords at the air in order to scare enemies away.
Revealing mistake: In the aerial shot approaching the Horse Kings village the banners are flapping the wrong way and the chimney smoke is going into the chimney, instead of out, revealing that it was shown in reverse.
Suggested correction: Which scene is that? I couldn't find it anywhere.
It's the scene where Eowyn exits the door angrily and walks towards the fire circle thinking, in the trailer she's on the left of the screen but in the movie she's on the right.