My biggest fear is that this "always-online" experience will eventually be plagued by trollers. A lot of the forum community is great, but the forum is a minority.
I fear that in the middle of a firefight I'll be fighting some Cabal on Mars, and then a guy drives up in his pike and throws smoke bombs everywhere to block my vision or drives his pike in front of me, or keeps doing emoticons in my face, or destroys my cover if I'm hiding behind something destructible, or if he has a cool rocket launcher (grenades, grenade launcher) that he keeps shooting at my face so I can't even see anything except smoke and explosions.
A game dependent on a co-op experience with random co-op encounters can easily turn into, (Let me go into the mind of a troll) "Who's game am I going to grief today?" I know it's been confirmed that a guy won't join your game and shoot you in the back, but it's still very easy to troll in different methods.
I'm pretty sure there could be countless other ways to troll (feel free to share/comment), but my biggest fear of Destiny is that this co-op "experience" could easily turn into a co-op nightmare.
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They could implement something like the mute feature we have on the forum. If you keep running into a player that proves to be annoying, you could add them to a list of people you don't want to encounter anymore. Something like that would be nice, but it's not like it would really stop it from happening again. I don't know what could be done to prevent it honestly.