Recently had a case where Tweet Blender didnt work correctly alongside WP Super Cache.
Tweet Blender showed the Tweets that was cached along with the page so in effect 3 weeks later you still have tweets from 3 weeks back showing.
The workaround was quite easy, All you have to do is refresh the tweet blender box as soon as the page is done loading.
So in your functions.php you add the following code:
After you saved that. Browse to the supercache folder delete cached file of the home page so the new script will be loaded.