More social stuff. The inability to talk to people in your fire team is beyond ridiculous.
Trading items, expanded eventually into an auction house.
The city needs to be opened and explorable, preferably with missions.
More options for unwanted gear. Dismantling is silly.
The ability to put bounties into your vault. Carrying an exotic bounty for a week and not being able to use that slot is a pain in the ass.
More randomness. Even if it's multiple spawn points for patrol missions. Spawning at the same spot each and every time is ridiculous.
Better bosses. The bosses in strikes are the laziest effort I've ever seen. Bosses that feel like bosses. Models that are exclusive to that one encounter, and not used anywhere else.
More diversified mounts.
Crafting system. I have a billion weapon parts and nothing to do with them. Even if it's just a temporary buff or whatever, give us other uses for them.
Consumables. Whether it's XP gain, damage bonus, or my personal favourite: allow materials to be visible on the map for a short time. Maybe one which amplifies the sounds that chests make.
To name but a few.