I ran into an interesting issue while trying to download a video in the background on the PlayStation 3:
There is content that has not been installed. You must first install the content to be able to perform a background download.
Since I just got the PS3 Slim (the price drop was the selling point), I started downloading several demos of games.
It turns out just downloading the demo is not enough, each demo must be manually installed. If the game under the game menu has a clear bubble around the icon, then the game has not been installed. I had five demos downloaded but not installed.
So the solution to this: install your demos and addons. Then grab a drink and wait, the install is slow.
Not exactly a good user friendly experience.