I really can't make many predictions about gameplay, because I am not a game designer and have no idea what would be within the realms of possibility of the 3DS's capabilities. But the way the shot is set up of Sora falling down to the ground in the Hunchback of Notre Dame world reminds me a lot of Mirror's Edge, so it seems likely that that world will require parkour-like gameplay.
I would very much like to see how Sora and Roxas, and Kairi and Namine, are dealing with their situations, since this is now an unprecedented moment of the Kingdom Hearts universe, and there could be a lot of interesting ways the story (and gameplay if they choose to use it for such) could go with that.
As to the Mark of Mastery exam, I don't have any speculation on the beginnings of it, but I think it would be interesting if Riku is the one to be given the title of Keyblade Master, if only because Sora is becoming a bit too much of a high figure. He needs to be taken down a few pegs in terms of power in the story, and there is nothing that says he can't still help everyone without being a Master. He could just get help from Riku from now on, or from Kairi, depending on the extent of what she can do as a Princess of Heart.
I hope Kairi will have more screen time in a new game, but I have no idea how this could be brought about right now. The trailer focuses on Sora and Riku and nothing about her, which is fine at the moment for a teaser, since she isn't a playable character.
Sora and Riku have to learn that there are people who need their help, since it was only data versions of them who found out in Re:Coded. This could possibly be learned over the whole course of the game, having different pieces of information going to Sora and Riku individually.
They also have to learn what the secret ending to Re:Coded told us, that since Xehanort's Heartless was destroyed before his Nobody, the real Xehanort can now come back. That's most likely why it shows (fake) Ansem and Xemnas at the end of the trailer, hinting that they are not going to be separated any more.
And this point is much more a wish I'd like to see granted, but I doubt will actually happen, but... I'd love to see Xehanort actually get Kingdom Hearts. Then KH3 (if it does in fact get made) can focus on saving everyone (if they haven't already been saved in KH3D, in which case, just rally them together) and stopping the full extent of whatever would happen after Kingdom Hearts is obtained from being carried out. The reason I think this would be an interesting idea for the story to take is because Birth By Sleep brought the characters as last minute as you can possibly get to stopping Xehanort, and the point of a series is to continuously be adding to previous installments. Have KH3D end with that as a twist, but still with a strong sense of hope that things can be saved, and then have the next game be about fixing this all with a big team of people. Basically, like Final Fantasy 6, but within a Disney-esque universe.