MoP and Cataclysm quest design leaves very little room to level a second toon without repeating most of the same content. I can level 4 toons of the same faction to 60 without repeating a single quest or dungeon more than once, and other than Hellfire Peninsula, I can actually get to 82 or so with 2 toons the same way. But it isn't possible to get through the last few levels on an alt without doing the same stuff every time - and often repeatedly with the same toon, if you're tanking/healing your way through dungeons.
It seems to me that there are two issues here. First, that in an effort to make questing feel more epic, they've also made it far more linear, and second, that a single toon's access to quests and dungeons while leveling is far too restrictive.
To resolve the former, I suggest designing quests to branch into a quest "tree" rather than having quest "chains". I realize this is a lot more work to put out an expansion, but let's be honest: most of the delay in putting out a new expansion is class balance and tuning. We all saw how quickly quests got put out during the MoP Beta, compared to class design. Not to mention that this opens up whole new avenues of storytelling that would probably make quest design easier in some respects. And it would certainly add to the replay value of the game enormously. Also, zones should be smaller - it feels bad to leave a zone early because you've outleveled the content. Which brings me to my other point:
To resolve the latter, what I really want to see is for each quest to be available to players much sooner. Gear is way better now than it was back during BC, but I never level through Shadowmoon because quests aren't available until after it's no longer efficient to quest there. I WOULD quest there at 63 or 64 and would be very refreshed by somewhat more challenging, and above all, DIFFERENT, content, but I can't, and by the time I hit 68 the content is no longer interestingly challenging, and Northrend is vastly more efficient even though I hate the opening zones there. The other important thing that would help would be for dungeons to be spaced more evenly through the levels. Levels 50-58 restrict your access to dungeons to just a couple that a tank might run 10 times, while hitting level 70 opens up a huge number of dungeons he'll probably never run at all. Neither of these fixes are hard - all this content is already in the game, it just needs to be spaced out so players have more choice about what to skip.
TL;DR Let me quest in Icecrown at 70 if I want, and design future questing zones to have stories where you make decisions that change the way you participate in them. This way leveling an alt is less of a grind and more of a way to get the "full WoW experience".