At launch people showed black flecks in VC games and advised to look for them the spot the issue. As I recall, ours seemingly had none in VC games.
I do recall that a GameCube game, The Legend of Zelda: The Wind Waker, had lots of white pixels in the lines where many of the polygons met in the environment when we tested with component cables.
We tested it because the same game with component cables on the GameCube had a strange artifact when passed through the image processor on the same TV (Sony XBR910). The dithered fog had a crazy moire effect that wasn't there on an XBR970 (tested in store with a battery-powered GC and rare component cables). As it turned out, the signal coming from the Wii was different in some way and the TV (XBR910) no longer had the strange moire artifact (yay!), but you would see white pixels in the environment (?!) which did not appear on a GameCube. You might see a few along where a wall meets the floor, for example. I haven't gone back to test but I think that was our first clue to the artifacts.
When we got Super Smash Bros. Brawl, we noticed some stuff in the menu background that we thought was just encoding artifacts in the FMV. You'd see a light gray spot appear every time a watermark in the background would spin to the same position, for example. We soon realized that it wasn't FMV. We noticed that the same flecks did not show on a friend's Wii and called Nintendo.
The thing is, we had a different Wii on launch day that failed right out of the box but Nintendo took care of us quickly and this was still a unit from the launch window (not sure if it was the RMA replacement or the one purchased a week later).