Personally, I disliked the Halo 1 remake, as instead of keeping true-to-the-game mechanics for the old game, they just hooked up Reach's multiplayer. I got to enjoy the campaign, but that is where the fun stopped. So, for me, I wouldn't want them to mess with any of the key functionality that Halo 2 had. All I would want is updated textures & models, perhaps audio & animation as well if they are so inclined. Beyond that though, no change. I want to be able to still bounce, lunge, and have the ever-so-rare encounter with the infamous ghost on Lockout. Days on end of Tower of Power on Ascension, Cat & Mouse on Coag, Boxing, Cops & Robbers, etc. I don't want them to mess with the formula at all. I would like the inclusion of Co-Op over XBL for campaign, though. (Only 2 people, though. Keep it classy, ya know?)
So TL;DR:
Change only the graphical elements mostly, and absolutely nothing that would impact superbounces, rocket-canceling, even the cheap button combos should stay. 100% True to it's roots, yet optimized for today's hardware. (Well, tomorrow's I guess; it would be released after the next generation of consoles)