I thinkthe addition of Gandalf's attack on weathertop and the later events of the Fellowship are great ideas
. If I'm turning this into a "what characters should PJ have included thread" forgive me, I'll try to connect them with the scenes.
Imrahil and Beregond events: Without these guys you miss two faces of Gondor, the strength, bravery, (and I might say styling knights of Dol Amroth), and the compassionate, caring, humble Beregond. Anyway, I would have liked to see these guys included and some of the scenes that they do. For instance, Beregond saving Faramir, or Imrahil telling Eomer Eowyn isn't dead.
The lords entering the City: One of my favorite non-fighting scenes in the book is when the outlying lords of Gondor, enter the city with their men, right before the siege...Forlong, Imrahil, Duinhir, Duihin, Derufin, Dervorin (you get the point), I just love that part
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Farmer Maggot's house: Farmer Maggot (since he did actually see Bombadil) played an important role in having the hobbits, in a way mature. He (as well as Bombadil) told the Hobbits they aren't the first to inhabit the Shire, and they won't be the last. They both taught them that there's a lot more out there then The Little Shire.