Some of my favorites are in the battle on Pellenor fields there is a hairy orc (facial hair) that the main orc talks to (don't know his name but pink guy with tumors) anyway he's at the gate then at the Rohirrim charge (obviously killed) then he appears at the landing of the ships when Aragorn arrives.
Another good on is at the black gate, many arrive on horses and in one scene you see them but in the next shot they are gone. I've noticed these and many others (it's kind of a passion of mine to find mistakes) but here's a fun website for those interested enough in it.
Link there are most all movies in there. You will find that LoTR ranks high on the most mistakes in a film.