How can I keep many old variations of the week on my computer?

yes you could save it to your hard drive, but I don't know if it's permitted or not.

You can save the the files by opening the media window (media page tab on the variation of the weeks page), and then choose appropriate type (i choose quicktime), and after the window come pop-up, just view the source of the page, and look for the address like :

http://www.dancevideo.net/Variation/variation.mov

ok, now just type this address to your browser and choose save when asked.

hope this can help, but trully i don't know it's permitted or not, and I think there will be a DVD release for the variaton, and that should be in higher quality.