Does an iTunes iOS device backup include everything on the device?
The backup contains:


All your settings
Application data except data marked as "cache" or not to sync.


Since iOS 5 there is a possibility for the developers to exclude some items from the backup.

There are ways to explore your backup, but I don't think this could give you definitive answer, wether your backup is complete or not. Developers should make sure that they don't exclude items from backup that cannot be recreated in some ways (download, rebuilding &amp; etc). Some movie players offer to disable backups for their content, but this is configurable.

Because TED content can be downloaded at any time, probably the developers decided to not backup video content. Check the app for settings.