Here are just a few simple things that are on the top of my list.
1. SPLIT MULTIPLAYER!
The community is clearly split between the old school gameplay and new gameplay, why not have both? Have Halo Classic Multiplayer (No sprint, armour abilities, ordanace and loadouts) and have War Games.
2. BRING BACK THE GOD DAMN MAIN THEME.
It didn't feel like Halo without the main thing (the theme being played for 10 seconds when you arrive at a Halo doesn't count). Marty O'Donnell brought the franchise certain rhythms which have become a ideology of the franchise. Props to Kazuma Jinnouchi, in my eyes he should have been main composer and given full creative freedom.
3. NO QUICK TIME EVENTS
No QTEs. Everyone hates them, enough said. Ruined a great build up to a boss battle.
When Cortana rises up from the Hard Light bridge, she should have damaged the Didact's armour so he couldn't use his "force-esque" abilities, that way Master Chief could have had a fair one on one fight, reminiscent of the battle with 343 Guilty Spark,
4. NO REPETITIVE TASKS
Halo 4 just felt like pushing endless buttons and putting cortana in various machines. In light of what happened in Halo 4, I can see this being different in Halo 5.
Apart from this, I do believe 343i get a lot of hate when they do deserve some praise. Look at the Master Chief for example, his redesign is amazing. They keep the core designs of his suit while bumping it up to be more practical looking. They also gave him a true voice, Steve Downes did a exceptionally good job in Halo 4, his voice acting has improved very well.
Good luck to the people at 343i for Halo 5, it's make or break to win the community back.