I finally had the chance to give the podcast a listen (it's been a crazy week). I think James and TYP pretty much understood what I was getting at. Greg's comment about the Star Road and Special World in particular encapsulate my meaning...although for Greg's sake I'm glad Johnny didn't read the part about how I treat Yoshi! I do have one addendum though: I forgot about New Super Mario Bros. (a bad sign in and of itself); World has that game beat in almost every way.
I hadn't seriously considered WHY World has that sense of continuity, but I think you guys nailed it when you pointed to the then-new save feature (and it's that type of insight that keeps me listening). The ability to take your time and come back to the game at your leisure also really helps the exploration aspect, since you're able to replay the red levels a dozen times to find the secret exit, safe in the knowledge that investing an hour into a single level won't stop you from beating the game later.
In terms of gameplay, I actually favor this type of play over the more arcade-style NES Marios, even if I miss the greater challenge that comes from that earlier style (and, I maintain, the greater imagination that went into the other Mario games, before and since). There is a strange trade-off, though, since I think that making exploration the hook can make the initial play longer and more satisfying, while simultaneously dampening replay value: I like the 3D Marios (where the focus is almost entirely on the type of exploration and discover that World created) more than the 2D ones, but I find that I can play all three of the NES more often without tiring of them. Am I the only one who feels that way?