Working from https://buddycloud.org/wiki/Buddycloud_HTTP_API#.2F:channel.2Fmedia.2F:media, it seems that I can POST a media item with a bunch of metadata, and I can GET the file itself, but there's no indication of how I can get the metadata for the file.
If I'm looking to display an icon for some files, and a thumbnail for images, it would be good to know the file's metadata information before attempting to GET it.