Some new info from Ruliweb...Some minor story/character elements involved, so I'll spoiler them just in case...
~ Some trophies will appear as Assist Trophies if you gain them
~ A boss in Subspace Emissary is from the Fire Emblem series. He does not fight but he summons monsters.
~ Boss rush mode after clearing Subspace Emissary.
~ You will need 240 hours to clear Subspace Emissary with every character available. [Bill: What? I'm thinking some slight exaggeration here, but to hear it's a lot is nice to know...Of course, there is the possibility that you can replay specific stages with every character after you've beaten SSE...]
~ Bowser, King Dedede and Wario also appear as bosses in the Subspace Emissary mode...They are being mind controlled
~ If you have a save data of SSBM you will get special trophies, BGM etc.
~ Same with Super Mario Galaxy and some other Wii games. [Bill: I've heard that you get Mario Galaxy music for having Mario Galaxy save data!]