David Storey advises over at My Opera. Put simply:

• Remember, even with the component cables, the Wii only supports 480p. We're talking circa 1995 resolutions.
• The Wii supports embedded Flash 7 (not 9) and has limited RAM compared to a desktop PC.
• Due to the Wii's limited resolution, Opera utilizes the same automated transcoding for both the Wii browser and handheld devices. For starters, it forces your site into a one column layout to prevent horizontal scrolling. Use a handheld stylesheet to override the automated reformatting and manually tweak your site's appearance. You might even look for "Nintendo Wii" in the HTTP agent header and send back a custom stylesheet.
• Use big fonts and take up the whole screen. Not everyone has HD.