Dude, continuity and Mario don't mix.
Technically, yes. However, I think Trainman's thinking more along the lines of "a mario sidescroller with references to a ton of previous mario games." That way, we can have some general continuity without having to make a super-complex timeline of mario events.
Some more ideas along that line would could be: a jungle level set on an island like Cortez's in Paper Mario TTYD. On the beach you could see Rogueport in the far distance, and as you went through the level you'd find the jungle with Putrid Piranhas, the famous rope bridge puzzle, the entrance to the pirate fort, and the pirate fort itself. You could also have a level set on the Isle Delfino, with Delfino Square as a background, Pianta park in the far distance, and Mount Corona looming over part of the level. The ideas are endless!
I think a cool thing to do would be for Nintendo to make a giant mario sidescroller for the Wii that takes elements from the 3-D games and RPGs. You'd have the Mushroom Kingdom as a hub, where you'd set off to all the other worlds - unlocking worlds as you beat bosses and saved villages. In each world there would be a village with a shop, inn, and other buildings. The health system would be a combination of the regular sidescroller system and the healthbar of Super Mario Galaxy. You'd start off full size, but if you lost two points you'd turn into small mario, who isn't as strong as regular mario.
There would be a TON of different powerups and items - including ones from Super Mario Galaxy and NSMB - but only a few standard ones that appeared in every world. Most would only appear in one or two worlds - ie. the frog suit would only appear in the water world, the Boo suit would only appear in Ghost Houses, and so on. Mario would start off with his jump move, but as he earned coins he would be able to buy new moves like the wall jump, ground pound, spin, and high jump. There would be a lot more worlds than in regular mario sidescrollers - I'm thinking at least 12 or 13 - and each would have a large world map with secrets and alternate paths. Oh, and the difficulty would start out easy, but get really hard by the end - instead of always staying around the same level like NSMB.
If Nintendo did a game like that, I would cry tears of happiness. :)