Actually I loved Firefly.
As for questions do you realize they only mentioned the elites once? And they didn't bother explaining at all though I guess if you played Halo 2 you're already know but if I was a marine at that time I bet I would have found that puzzling to say the least or thrown a question out about it. ODST takes place when the elites are fighting the brutes and losing and they really didn't show that in game.
Two, the brutes are now riding on freaking jet-packs now which is freaking stupid to say the least. Not to mention how weak the brutes are now. The brutes wiped the floor with the elites but if you played this game you're wonder how that possible since these mindless monkeys are nothing more than cannon-foder.
As your theory about burial the humans--the don't bury them because to them the humans are nothing but heretics. That's why you never see them using human weapons ect. Also the Covenant have glassed numerous human worlds at this point so the people wouldn't exactly brother fleeing from one city to the next, they would head to the nearest hanger and look to get offworld ASAP.
And I DID compare the game to another video game--Dead Space. Just because it's a video game doesn't mean the plot has to suck ass. Sure it's not the Worst video game plot but consdering the money Bungie throws at it's games you'll think they can do better than this.
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What would I have done with the game? I'm glad you asked

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For one I would have shown alot more all around fighting in the distance, between the brutes vrs elites or brutes vrs humans. And I would have left alot of civilains in as well--for one you can have side-missions where you have to help them escape or even help them fight. Like I stated before the Covenant glasses planets so I assume some civilains would rather fight than simply die.
Two, I would have made the main characters alot weaker--you shouldn't be able to knock the **** out the covenants all on your own. I either would have an endless horde of respawnable soldiers helping out (think Call of Duty 2) or maybe a tighter unit (Left for Dead), hell of even a Band of Brothers cover system. So instead of marching into a horde of Covenant you're be setting up ambush points, setting traps, or laying down coverfire so your team can flak them. Yeah it would change the gameplay quite a bit but at least you're feel more human than super-spartan anyhow.