Well, for starters, we can just throw up our hands and give up on random five player content until Warlords, when DPS players will be destroyed by the new dungeons if they pull too hard and tanks will have to learn they are not actually from the planet Krypton (at least for the first few months). While I don't believe that the new silver Proving Ground requirement will fix these kinds of issues, it'll be in place, and heroics will be on their own progression tier, so perhaps we'll see less people chain randoms for valor and more people who are there because they like actually playing as part of a group.
Because it's group play that five player dungeons are meant to require and reward. Not 'look at what a superhero I am running ahead to pull the entire instance' play - that's basically soloing, and it's not for when you queue up for random dungeons.
Now, sometimes you get a group where everybody is geared and everybody can do ridiculous damage (including the tank and healer while healing) and you just storm down the place like the scythe of destruction. And that's great - if you're all on board with it, chain pull to your heart's content, demolish your enemies and leave their broken corpses unlooted behind you. (Seriously, why do people do this, pull the entire dungeon into an AoE pile of death and then not loot it? It drives me nuts.) But frankly, it's worth the twenty seconds it will take to find out if that's the case. It's worth asking. It's worth communicating with your fellow players and making sure everyone is on board.
I've had runs where the tank has looked at my gear and said "Go nuts, I can handle it" and she did and it was great. I've had runs where I ended up tanking the whole thing because the tank assumed he or she could handle it and started running ahead and pulling everything. If the tank pulls like they can handle anything without any communication, I assume they can, because if they can't, I probably can in most heroic dungeons the game has now. And as a tank, I've had that DPS player who just wont stop running ahead and pulling, and I've seen them survive (usually due to a couple of heals tossed their way) so I know how frustrating it is from all sides. The real solution is to talk to each other, but it's hard to motivate the uncommunicative and the self-absorbed to do so when all the dungeon content we have now is so out of date by this point that it simply doesn't require any group cohesion to make it through.
Not having additional five mans past launch turned out to be pretty destructive to the random dungeon player, because without escalating difficulty queueing has become completely a game of gear disparity. It always has - even back in Wrath of the Lich King players could often totally dominate a run if their gear was good enough. But what Wrath and Cataclysm did right (especially Cataclysm, which doesn't get a lot of credit nowadays) was in introducing more five mans that were harder, that asked for more group play, that forced even the more antisocial players to make an effort to be part of the team. Sure, by the end of Dragon Soul gear was starting to make the Hour of Twilight dungeons less difficult, but the order of magnitude this time is extreme - it's over a hundred ilevels worth of gear difference.
Warlords will bring the item squish and new content tuned to be harder for us, and that'll force some players to learn how to talk again. Until then, though, we can but make the effort ourselves. Learn to throttle your DPS if the tank is undergeared and making an effort to perform the role. Learn not to run ahead and pull the entire dungeon just because we can tank it down and outDPS the entire rest of the group combined just because of Vengeance. In general, while we wait for Warlords we need to make an effort to relearn civility.
If you want to solo things, just go solo them. If you're signed up for group play, play with them, don't be an obstacle to them.