AFAIK the Wii doesn't have patches or updates of any kind for its games. Is this still true for Wii U?
Yes, the Wii U does in fact patch games if necessary, the Wii did too.
The thing about the Wii was that - just like with the 3DS - users would need to download patches manually, as if they were DLCs. One such patch was released for The Legend of Zelda: Skyward Sword.
The Wii U can patch games automatically. One such example would be Pikmin 3.