The other two changes are harder to spot by the viewer given their total absence from the films.
The Scouring of the Shire
In the books, Frodo and Sam destroy the Ring, are rescued by the eagles, and return to Rivendell. After a number of farewells, the hobbits leave on their own to go back to the Shire, to breathe the fresh air of home again. The reader prepares himself for the cathartic ending, prepared to view the idyllic hills of Hobbiton once more.
But it quickly seems as if something is wrong. When the hobbits stop in Bree to rest and see how Barliman Butterbur is doing, they hear of the presence of Southern thugs in the region. Not all is at peace. That rest that they were all looking forward to will have to wait. They leave Bree and push on to the Shire.
To the horror of the reader, we see Hobbiton burnt and ruined. The grass of the hills burnt to a cinder. The cheerful, happy cries of children replaced by emptiness. Once boisterous hobbits are bent in drudging toil, working endlessly in factories belching smoke. If ever there was an allegory for terrible industrialisation, this is it.
As it turns out, Saruman, after being exiled and released from Isengard, decided to be a dick and ruin the homeland of the main characters. While this is an unmistakably dark event to be confronted with after the victory over Sauron, it is in perfect alignment with Saruman's character. Saruman is always portrayed in the books as the supporter of science, technology, and industrialisation over all other factors, often to the doom of himeself and those involved.
But this event is conspicuously missing in the movies...
Why the Absence?
Amusingly, there are two events in the movie which foreshadow the Scouring of the Shire, despite its inevitable absence from the story. In the Fellowship of the Ring, Frodo sees within Galadriel's mirror the enslavement of the hobbits and the ruinous future of the Shire. In the Two Towers (extended edition), Merry and Pippin raid Saruman's larder and find barrels of pipeleaf from the Shire. In the books, the reason Saruman has the pipeleaf is directly linked to his domination and ruination of the Shire. In the movies, this is merely a plot hole.
In the end, it seems evident that Peter Jackson and the screenwriters did not want such a disturbing event near the end of the trilogy, particularly after the arduous and intense trek up into Mount Doom, the severing of Frodo's finger, and the death of Gollum. This seems fair, as the razing of the Shire, one of the most beautiful and comforting places ever seen in cinema, would be immensely discomforting, and would leave the ending with a sour note.
This picture is beyond words.
When travelling to the village of Bree from the Shire, the four hobbits (Frodo, Sam, Merry, and Pippin) encounter in the Old Forest a mysterious character. Saving them twice from harm, Tom Bombadil, a peculiar and whimsical man, takes them to his home to give them some measure of safety and solace before they go onward in their journey. He is unique in his very strangeness. He does not appear to truly fit into the world of Middle Earth. Tom speaks in musical rhyme and without care, confident in himself and his place in the world. Twice he saves the hobbits from dangerous harm, from a giant tree and ancient buried evils. Both times he does it with barely any effort at all.
Tom Bombadil is intentionally written as an enigma, a character whose power and purpose in the world is unknown. The One Ring holds no power over him, and is the only character in the trilogy to put it on without turning invisible, instead laughing at it and then consequently finding it unimportant. This is an effective jaw-dropper for the reader. The greatest threat in the book is rendered irrelevant and without power by some random old guy in the woods... It is clear that he is an entity of immense importance.
But, in fact, after this encounter, he ceases to hold any real importance within the trilogy. The Council of Elrond considers having him care over the Ring, given his unknown power and his immunity to it. But then they decide that this would not do, as he would attach no importance to it and would likely misplace the thing. For Tom Bombadil does not think or act like others do; his is a personality and character that is wholly unique and wholly unreadable.
Why the Absence?
In essence, Tom Bombadil's presence is replaced in the movies by Gandalf's imprisonment and escape from Saruman, events not detailed in the books, only mentioned and hinted at. The rationale involves keeping the story at a fairly good pace; Gandalf's interactions and battle with Saruman are understandably more dramatic and active than an encounter with the musical rhymes of a mystical old man in a forest. Peter Jackson points out that Tom Bombadil doesn't actually do much to advance the story, and thus he was bypassed in the interest of "not making the movies too long".
This is a fair judgment. While Tom Bombadil is a very interesting character with myriad possibilities, his creation by Tolkien was an act of world-building; a character who helps bring detail to the world but does not actually move the plot in any form. Consequently, for a movie that turned out to be an already lengthy 3+ hours long, his absence helps save the viewer from another half hour without using the restroom.
But to those intrigued by Tom Bombadil, he is one of the most interesting mysteries of Tolkien's universe, and has been regarded as God, an angel, or the incarnation of Mother Nature herself.
Of these differences that I noticed, only Faramir's change in character seemed to have a negative effect on the trilogy as a whole. Taken in all, the films are fantastic and with almost no faults. But so are the books, and it is interesting to note differences between the two and why they occurred. For those who haven't read the books, I highly recommend them, and you will encounter a Middle Earth with more detail than you can imagine. And for those who haven't seen the movies (the two of you out there), they are, for the most part, Tolkien's vision brought to life.
And watch those special features! They are enjoyable and thought-provoking on their own!