Namely, the portrayal of the Covenant. I used to think of them (since I had never read any Halo novels) as a utopian society that humans could never form. So many different races, united by one ideal. In Halo 2, the Covenant are human beings with different physiques. They speak english better than most people I know. As I learned of the Covenant, they became all too familiar. They became boring. They were not either an alien group to admire, or to fear. I'm also rather dulled at the campaign. Switching from the Arbiter to the Chief and back made me lose interest in either and playing from the perspective of the Covenant made me, again, become too familiarized with them.
In the first game, I disliked the Flood. In Halo 2, I'm introduced to the Gravemind and I feel like I'm being laughed at. Why is this piece of vomit here?
The only aspect I didn't like in Halo 1 was the religious reasons for their assault, I would have much rather have had them consider humans for the Covenant, but them disdain us as beings incapable of holding such a position and not only that, but as an overpopulated race that threatened the balance of a galactic ecosystem. So, they decide to pwn us. In Halo 2, their religion is given even more emphasis.
I'm certain I'm forgetting a few things, but I suppose that mild explanation can do for now.
As another minor nitpick, however, the Jackal snipers in Legendary are ridiculous.