Considering that OpenGL 1.3 (defined in 2001 I think it was) already had dot3 texture combining, that would make doing diffuse normal mapping trivial, and I would be AMAZED if the Wii couldn't do it.
Anyway, normal mapping has so many forms. Most games today implement some kind of virtual displacement (done in a pixel program) to make bump mapping actually look 3d. The Wii has no chance of that sadly, but an environment map for specularity added to simple OpenGL 1.3 dot3 mapping will still look pretty decent.
Real time shadowing with shadow maps? Well OpenGL 1.4 had that as part of it's spec around 2002. The Wii MUST surely support it then. Of course they won't be able to do any of the multi sampling on shadows that can be done on newer hardware, but they can make a good shot at it.
I think the real killer for the Wii is no floating point texture support, so that that means true HDR is out of the question. HDR is really what makes games like Uncharted 2 shine IMO.