What you are experiencing are the symptoms of your GPU getting too hot. You'll start to notice it in games that graphically push the Wii hard, but eventually you'll get these anomalies in the main menu, in VC games etc
The cause is leaving the unit in Standby / Connect24. The wireless chip set generates a lot of heat that contributes to the GPU overheating. Nintendo will acknowledge this is an issue.
I believe it only affects launch models. I also believe that a recent firmware update spins up the fan every so often when the Wii is in standby so as to keep it cool.
Nintendo will replace your console, you only need send them the console itself, nothing else - no peripherals.
I got my Wii at launch in the UK and by April time had the same thing happening. It started when playing Zelda and got worse over time. Nintendo acknowledged the problem and replaced immediately giving another warranty.
Do a search on Google for "Wii GPU overheat"........................