Wii Mini could negatively impact Wii U
While their two competitors are moving forward with new hardware for this holiday season, they're going backwards -literally to the previous gen. How about some more energy and hype into all of the promise and potential that the U could offer? As it is, last I heard, EA and 2K both have no current intentions on publishing for the U. So now the game selection is slimmer than it already was.
If the Wii mini does sell, it's really a win-win for Nintendo, since it's unlikely to cannibalize much of the Wii U's sales (most of that loss will be uneducated parents and grandparents who buy the "new Wii" for little Janey and Johnny). There are plenty of Wii games out there on the market to build a strong game library for it. The lackluster Wii U library, which as you point out is missing a lot of big publishers, is not an issue. Additionally, since the Wii mini lacks internet access, Nintendo doesn't have to worry about supporting any online features and can continue shutting them down to save money.
However, we still advise against buying a Wii mini; it's not a good piece of hardware and you can pick up a used Wii for a song nowadays.