Granted, I don't know that much about networking, but it seems to me that if Nintendo were smart about it, they would have realized that wireless networking is not quite at the plug-and-play stage, and they'd have made allowances like the other two for wired networking as well.
After two hours over a couple of days of "troubleshooting," which basically means trying different things that don't matter because if one of them worked, the others would have worked too, my conclusion is that Nintendo put in a decent wireless card, but disabled most of the features that make it work, so that connecting your Wii to a properly-secured network changes from a moderately easy task to an extremely difficult task.
The concept is really simple: once I knew what I was doing with respect to the router, I got my laptop connected easily. Set the SSID, choose the encryption, get the right passkey, enter that information, poof, done. All the time that I'm jacking around with the Wii, my laptop figures out what's going on and connects itself each time, as I'm changing channels, broadcasting/not broadcasting the SSID, etc.
But on the Wii, no, not simple. Apparently it only works under all of these specific circumstances. Whatever. I'm thisclose to simply letting it stay disconnected until Nintendo figures out wtf is going on. I'm not interested in weakening the security of my network because Nintendo doesn't know how to do networking.
And isn't a USB-to-Ethernet adapter going to cut down on connection speed?