Movie Mess Ups

In the Two Towers there are a couple of somewhat obvious mistakes.
1) Pippin and Merry get captured by Uruks, and the Uruks get attacked by Eomers men. During the battle, the hobbits escape, and during the escape, Pippin almost gets stepped on by a horse. He is laying on his back, and the horse rears up, and Pippin's tied hands, are magically untied, next time you see him, they are tied again.
2) When Aaragorn and company first meet Eomer, they have a long chat, and then Eomer leaves. But when Eomer gets on his horse, his sword falls out of the scabbard, he then ignores the missing sword and rides off.