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The YouTube Channel on Wii was a surprise to even see. Google has been making a number of changes over the past 8-10 months, and after a period of time where it was unwatchable, some recent changes have made it better for many users. For me, the playback has gotten much better than the situation you describe, but there are annoyingly long load times. What I suggest is deleting the YouTube Channel from your Wii AND going into your save files to delete YouTube save data as well (you use the button on the bottom left of the screen to access this - if you need detailed instructions let me know and I will do it step-by-step). Then go to the Wii Shop Channel and redownload YouTube. There is no guarantee that this will work but it might.
There is a thread on this in Google Product Forums, so you are not alone. Check it out here: http://productforums.google.com/forum/#!topic/youtube/g1Eqi6v2as0[1-25-false]