Ok, a couple of things:
1. Remove death animations-They look too fake/Hollywood. I think the only one's should be assassinations and the classic one where you swing your arms and legs in the air after being blown up (Hilarious!) The result would be a more fluid rag doll like effect, Halo 3 comes to mind...
2. Have a classic slayer game type (and maybe a classic objective)- Classic should involve everyone spawning with the same weapons (AR/BR/DMR and pistol), no Armour Abilities (power ups on map), no instant respawn (which BTW was a great idea, but just not in classic) etc. Also, (and this applies to non classic) REMOVE KILLCAM! It is broken and should never have been involved, wrecks good sniping spots.
3. Elites & Dual Wield-'Nuff said...
4. Team work-based game types- E.g Invasion. Very team work-based.
5. I know it's very cliche to fixate about Halo 3 (It was my favourite game ever though, not just Halo franchise) but something about Halo 3's physics and rag doll just seamed very VERY realistic and something about is was just so awesome, for lack of better word.
Oh, and if you guys end up making Halo 2 (and possibly even Halo 3) remake(s) please, PLEASE remake the multiplayer as well, don't keep the current Halo's multiplayer. That is all. I hope 343 actually looks at this page and takes notes!