When Legolas, Aragorn and Gimli are talking to the Rohhium, Eomer's sword falls out.
When they are crossing the Plains of Gorgoth. The scar on Frodo's cheek switches sides.
When Gimli is telling Eowyn that Aragorn fell. The blood on his ax disapears.
When Merry and Pippin are watching the Rohirrum attack the Urk-Hai. Pippin's hands become untied then retied.
When Sam kills the orc that was going to kill Frodo, Sting has no blood on it.
The picture in Rivendell, of Isildur cutting the ring off of Sauron's hand. In the Hobbit the ring is on Sauron's finger. In the Lord of the Rings the ring is gone.