I had to set the Wii to 480i for it to work, otherwise it flickers and loses sync with my Sony Bravia TV. When set to 480i it works great. So I am thinking that there is a conflict between the 480p output signal of the Wii (1st gen, the one that plays GameCube games, too) and the adapter.
From what I can tell, the adapter wants a 480i signal because it wants to convert to 480p on its own. Then it sends the 480p signal down the HDMI cable to the TV. I am pretty sure that this is a correct assessment because I have tried it with 3 different TVs (an LG and a Vizio also) and got the same results.
This should be explained in the documentation.
Aside from this one caveat this adapter works GREAT-- once you set the Wii correctly to 480i (NOT 480p).
This issue wasn't enough to deduct a star, so I didn't. But they really should explain this to people, it would save them some headaches getting it set up.