Probably integrate flying and undersea travel from Mario Kart 7, bikes from Mario Kart Wii, and have additional modes utilizing the Gamepad.

i dont think they will do alot of stuff with the controller. people buy mario kart to play 4 play split screen, if they give a lot of features to that one person who is holding the tablet and leave the others who are playing with other controllers that wouldnt be a good call

There has already been a thread like this.
Double Dash 2 was what I mentioned. Using the GamePad to aim and throw items while the other player drives. Battle mode options, etc.

+1 for asymetric gameplay^^

Depends on how they do it.

If the player with the Upad is playing it differently - that is, if their goal is different from that of the other racers, then it would work quite well.

For instance, what if the Upad player has the goal of preventing the other four from winning, and can do things like take control of any of the computer characters, manipulate track features, etc? Basically, the Upad player becomes the malevolent game AI, doing everything it can to destroy the other players. Of course, on the flipside, the Upad player could be a supporting player, helping the regular players to defeat the computer, too.

That sounds pretty sweet, but how would it work with only one Gamepad? If you wanted to do 2 vs. 2, one of the teams wouldn't get the Gamepad advantage.

@OP: I think the Gamepad will be used conservatively in Mario Kart Wii U. Acting as an additional screen would be ideal since it would allow a fifth player to join each race. And maybe it could work as a rearview mirror during single-player action. Other than that, I don't know what else Nintendo could do. Maybe an asymmetrical multiplayer mode where the Gamepad player can manipulate items in a battle arena or something?

Make it like the N64 version, with HD graphics and a track list like the DS version. That's it.

Don't, please, don't make it like Wii, GC or 7. Balance and depth is what they should focus on.

2 things i feel i should point out about it
1) Retro arent making it as i saw somone post that they dont want that, watch the nd
2) by the time its released 2 gamepads will be in use so all 2 gamepad ideas will be brilliant such as double dash 2 or local 6 player
also give us clans and clan wars with oice chat, would make it alot more convinient

So they should focus on balance and depth by imitating a game with some of the worst rubber banding in the history of gaming?

^^^This. You might aswell be asking what direction will the new 2D mario take.

I do hope though that they try to increase the sense of speed and intensity of the races.