I think it would just be best to dispense with plane-walking entirely in Dark Sun. The original Dark Sun cut huge numbers of monsters from the setting, and most of those match up pretty well with the new planes. Dark Sun needs giants, desert creatures, insects, carnivorous beast and abberations as its monsters. Even undead aren't particularly noteworthy, except for perhaps the Athasian fast zombie.
Warlock and Paladin are the trickiest classes to fit into the game. I think a case could be made for both of them being Templars, which might mean that a new hybrid class to replace both of them might be in order (a leader/blaster). Clerics are out, but now you can use Warlord to compensate. The Druids aren't in the core rules, so I guess it is a question whether or not someone considers druids essential to Dark Sun. I would perhaps wager that they aren't, simply because it detracts from the theme of magic killing life.
Psionics would be interesting in a 4e context given that it was promised that psionics would have a niche that wouldn't replace other spellcasters. So perhaps it will largely be based on telepathy, psychic attacks, body buffs, and soulknife-like abilities.
I can't see any way of integrating tieflings and Dragonborn into Dark Sun. Dragonborn might be possible if they were more like lizardmen, but Dragons are unique creatures in Dark Sun, so the whole theme and backstory of the Dragonborn race simply doesn't fit.