1. Balin emerges from the depths of Moria, claiming he "fell asleep in the tub".
2. Galadriel discovers Pippin singing the praises of a bath while he takes one in her mirror.
3. Boromir uses the ring, saves Gondor, destroys Sauron and becomes a wise and benevolent ruler. Book ends 40 chapters sooner.
4. Orc-slaughter competition between Legolas and Gimli becomes so fierce, they take to killing some of the smaller, uglier men of Gondor.
5. Farmer Giles of Ham shows up at the Pelennor Fields and saves Gandalf's life.
6. Pippin hits on Eowyn in a dark corner of the Houses of Healing: "The hands of a Hobbit are the hands of a healer too, you know..."
7. In the happy days after the defeat of Sauron, Gimli keeps his promise and visits Mirkwood with Legolas -- where they are eaten by giant spiders, whom everyone had forgotten about.
8. Aragorn discovers that he is not, in fact, Elendil's heir. His older brother Mutt, after having lived with Ghan-Buri-Ghan & Co. for decades, lays claim to the throne after all the "dirty work" is done.
9. Ents and Elves dispute over title of "first-born". Elrond has Quickbeam made into an armoire; Treebeard grinds Glorfindel into mulch.
10. The Shire, mobilized by Merry and Pippin and now hungry for vengeance, annexes Bree and slaughters "the big folk".
Special bonus plot twist:
11. Gollum adapts to molten Mt. Doom environment, and later plays a critical role in Fourth Age crisis.