If one uploads files through Picasa whose file name contains several dots (that is, not only in the extension ".JPG", but as "DSCF9661...JPG") are not downloaded into the Brilliant Gallery, thus not displayed on the drupal site. This applies to any image sizes (original preview or thumbnail).
I used a picasaweb RSS feed for importing the gallery in Brilliant Galleriy. I suppose the bug originates from a wrong RegExp or an improper file extension handling in the BG code.