Here is an idea to improve the console itself. They could release a redesigned version much like Sony did with the redesigned PS2. In the redesigned Wii, the main change would be the graphics card. Unless I missed it, I don't think I've seen that mentioned in previous posts yet. One of the biggest drawbacks to the current Wii (as much as I love playing it) is that the graphics don't look as good as they could. As PC gamers know, the same game can look considerably better when you upgrade your graphics card and reinstall the game. The Wii has an ATI graphics card that works fine for the virtual console stuff but that can't really handle 3-D graphics in the disc games very well. They need to work with ATI to make a graphics card that does anti-aliasing at least, if not also doing a better job of rendering textures and bump-mapping. ATI has video cards for laptops capable of better 3-D rendering than what they put in the Wii that could be adapted for use in the console.
Also in the redesign, I would make the Wii a little bigger. There is no real reason why it needs to be so small. If it were, say, twice as big, you'd have more room for better heat management which would allow for faster processors (both GPU and video card). It would also allow for having more parts inside the console instead of having to plug them into it. It's like those tiny, thin notebook computers you see now. They are really small and cool looking, until you plug into them all the drives and accessories you need. Then they start to look messy.
As much as I like the Wii Remote idea, it is just too different of a form factor for a lot of people. I'd redesign the Wii Remote to make it more like the game pads that gamers are familiar with. I know the idea was to make it more like a TV remote to appeal to non-gamers. That idea kind of backfired though, because a lot of gamers don't like the design at all. If you play games using the Wii remote without any of the skins or adaptors that have been made for it since, it really is rather uncomfortable after a while. It could be more ergonomic than it is. In some games, it's hard to hit the tiny + and - buttons fast enough. That's why the classic controller and third party controllers like the Thrustmaster one were made, I know, but those controllers don't have the motion sensing that the Remote has. If the Remote had been made to look and feel more like the Thrustmaster to start with, it would have been better.
It would also come in more colors than just white. White is about the worst color to make anything you are going to handle on a daily basis. It's hard to keep looking clean as it shows every fingerprint and mark. It should at least come in black if not other colors like dark grey (my favorite), red, blue and orange.
Finally, I'd make the motion sensing technology more advanced than it is. It's pretty revolutionary already, but as other posters have pointed out, it's not quite the 1:1 motion mapping that gamers were hoping for when the console first came out. Some games like Dragon Quest Swords come close, but still aren't quite there yet. There is the new sensor bar coming out that newer games will be compatible with, but it should have been with the console to start with instead of making gamers buy yet another part.
I like the Wii, but those are some changes a redesigned Wii could have.