I ran into some trouble with Brilliant Gallery on my website (Drupal 7.22, 'hosted' on WAMP, Touch 7x, 1.7 as default theme). When I use the [bg|link-to-picasa-rss] tag, the pictures don't show in my blog post. The only thing I see is a list of are grey dots (so filtered HTML recognizes something in that bg tag). I checked sites/default/files/brilliant-gallery-temp and there is a folder present in which the images from Picasa are downloaded. So Brilliant Gallery is partially working. But that's where it stops. There is no folder with resized pictures to be found. I tried to switch from Lightbox to no overlay browser in the configuration of Brilliant Gallerie, but the result stays the same.
My guess is that something goes wrong somewhere between fetching the images from Picasa and resizing them for display.