"Return of the King" is on my TV right now. I happened to turn it on at the point where Frodo and Sam are almost to the Crack of Doom, and Gollum attacks them. I watched for only about 10 minutes or so. Here are the errors I noticed:
1) At the edge of the Crack of Doom, when Frodo is standing there with the Ring and says "The Ring is mine," he leaves out the beginning: "I have come, but I do not choose to do what I came here to do." Okay, it's a little thing, but I noticed it. Mainly I was waiting for him to say it because there was all this close-up camera work on his face, and I'm like, "Say it! Say it! No, wait, you only said part of it."
2) When Frodo puts the Ring on his finger, the armies of Sauron are supposed to falter, as if suddenly bereft of direction, as all the will of Sauron is turned towards the Ring. But instead they keep on fighting.
3) Gollum dies because after he bites off Frodo's finger, Frodo attacks him again. The two of them go over the edge, but Frodo manages to hang onto the rock. Wrong! Gollum is supposed to go over the edge by himself, from dancing with excitement.
4) When Frodo wakes up in Ithilien, he is greeted in bed by the entire Fellowship, including Sam. But Frodo is supposed to wake up before Sam, and then fall asleep again waiting for him.
I should explain that I can't even remember the last time I read "Return of the King" -- it's been years. But I had it practically memorized when I was 13 or so, and obviously I still remember it very well, and don't like changes.