Many people find the out-of-game community cumbersome. I'm not sure what has been explored in terms of in-game social activity, but I think it's safe to say there isn't much of it besides what's been pre-determined outside of the game. In some cases, the game actually discourages being social.
If I want to join the fireteam of someone I see doing the same story mission, when invited I have to go to orbit and come back to the instance, and before I can speak to them over game chat to see if they seem like someone I want to run with. Utilizing the xbox UI for sending messages and initiating chat is cumbersome when it involves someone not on your friends list and gets in the way of playing. I'm assuming these types of things could be streamlined a bit. Mic indication and gestures for yes and no would be very helpful, as well as proximity chat and overall better integration with the console's social functions.
I would like to form friendships based on common experiences within game, but besides joining matchmaking and talking to myself during a crucible match or ROC strike in hopes that someone will hear I have no idea how one would get started.
Destiny is the first game that compelled me to make more online friends. It's the reason I joined reddit. I've had success meeting people here on reddit, and started meeting more friends through those friends. Seeing what they're up to and if they have any fireteam openings requires a bit of interrogation but is manageable. On the roster screen, showing what our set destination in orbit is and having that display as "Queued: Crota's End" or something similar may be good for people that have a lot of friends. It could also show friends that are in orbit queued for activities first.
Though I've acclimated, I think many are not accustomed to the level of social involvement ultimately required for access to everything the game has to offer. If there is a way social interaction could be more naturally incorporated into the in-game experience I think there would be a lot more involvement and it would better the community.
Sorry this ended up longer than I would have liked, but hopefully you can find some value in it.