Real-time weather could be done over the internet, it is on many PC games. Although I think this would increase loading times and would be kind of a hassle (except obviously you would be able to turn it off since not everyone was an internet connection on their wii)
I think it would be better if there was weather that just kind of changed randomly during the battle but didn't use the wifi
I think it would be sweet if using the internet connection the released to event matches every so often that you could save to your sd card if you wanted to keep it for after the week was over and the new one was out.
This would also allow them to sell "event match sets" on sd cards in stores and you could buy sets of like 500 event matches for the price of the sd card and however much more they think is reasonable