I wrote a really long comment but it was killed by the server gods. So here is an abbreviated version.
I think the first game did some cool stuff that no game has really done since:
1. Open-ended levels design. See the last part of Assault on the Control Room, where you gave the choice of traversing normally, jump down onto the pyramid and skip some parts, or stealing a banshee and destroying everything in you path and skipping the rest of the level. There are a lot of these scenarios in the game, which makes it really replayable and puzzle-like.
2. Few but varied weapons. Since you can only carry two weapons and the encounter types varied a lot, this made planning important and made for interesting and replayable combat. Probably not apparent unless you play on harder difficulties. Bungie left this less-is-more mentality already in the second game.
3. Large, open-ended encounters (especially on AotCR and Two Betrayals). You find yourself having to play the covenant and flood against each other, and clean up what remains.
Also: Crazy moon physics on the vehicles is the best and made for some great custom multiplayer modes.
Anyway, I really enjoyed your text. As someone who has played a lot (arguably too much) of the first game, it is hard to remember what parts I didn't like about it the first time I played it. I look forward to your thoughts on Halo 2. I pretty much hate it :P