I expect that Nintendo will use this feature well, but I see two potiential problems with it:
1. Security. Obviously, if the Wii is pulling content, what is stopping someone from tricking it into downloading a virus that deletes all of your save games? Nintendo will be signing everything, I am sure, but I hope they future-proof/over-engineer it because encryption/crypographic signing that is good now is often worthless ten years from now. (I am assuming that it will be pulling/acting as a client because otherwise NATs would cause problems. I guess it will just keep a socket open to Nintendo's servers... which would require a lot of server CPU cycles and bandwidth from Nintendo and could give them a lot of information (just how many Wiis are connected would be big marketing data).)
2. Patches. Put simply allowing patches means allowing unfinished games. I see this as encouraging patches. I remember some people complaining about games on XBox being released buggy and getting patches later because it has the hard drive. Although, I guess with half a gigabyte for everything the system has to store, the extra info can't be huge. Once again, I do not expect problems in first party games from this, but third parties do worry me.
On the positive side, hosting personal content via ones personal Wii would be nice for Nintendo.
Also, two words: Bit. Torrent.
Nintendo is not stupid. They will have a huge Bit Torrent swarm for anything they want to pass along to every Wii.