With the visuals they should continue to make everything super realistic looking to contrast with the abstract looking Pikmin. I think they could make the Pikmin look like they are done in claymation.
Most importantly to the next Pikmin is online.
Instead of controlling hundreds we should control thousands of Pikmin with many new types of Pikmin. Are there any Pikmin that can tunnel in Pikmin 2? What about flying Pikmin? Really fast running Pikmin? I really want Pikmin that can walk up any surface, even upside down. I never liked the Pikmin that threw bombs, I always thought why didn't they just make the barrier simple enough to be burned away so the yellow pikmin could be pikmin that expell fire. How about Pikmin that are strategical, they grow a bunch of leaves on top of their heads like a deku shrub, and then when an enemy turns around to look when it hears a noise they all drop down and look like a bunch of moss or little bushes. You've all seen the gag in cartoons before, the villain is looking for Bugs Bunny and Bugs is hiding in a bush walking behind him. Some Pikmin could glide, some could fully fly. Some could be combonations of different Pikmin that result from the player's decisions on cross breading Pikmin. Pikmin that could climb right up a tree and then glide from where they decide to jump. Imagine thousands of Pikmin coming through the woods like an army.
I'm sure voice recognition controls will be involved in the next Pikmin. I wonder if there will be a Pikmin game on the DS?
I don't like the space dude that we play as. They need a new character to come discover the Pikmin. Some character that could be more marketable to older gamers as well as young gamers.
A new controller featuring mouse functions or wireless tilt sensors in addition to traditional analog sticks and face buttons will allow for better control over the characters. For one, the camera would be better. You could not only direct the Pikmin with voice commands but also with hand gestures if the controller can simulate what a mouse can do.
What the next Pikmin needs to do as far as enviroments is to give us urban landscapes. Country houses, suburban areas, sewers, cities, and parks in addition to the areas in nature. I didn't play Pikmin 2 yet, I have no idea what enviroments it has, but I'm sure you aren't trying to get a hundred Pikmin across a street while traffic is coming.