factual mistakes about The Lord of the Rings fostered by Jackson's movies

These are specific errors, not general falsities of spirit, and they have in common that people don't realize they're major changes from the book. When the movies omit Bombadil or the Scouring, or have Faramir threaten to seize the Ring or Frodo abandon Sam, viewers realize those are changes. But they fail to recognize that the following are not true of Tolkien's story:

1. That Sauron, at the time of the War, is a disembodied giant eyeball.

2. That Aragorn is reluctant to become king.

And the latest additions,

3a. That Smeagol is a different character from Gollum,

3b, and is basically good.