That's very mysterious indeed since regular collections (with the blue icon) should always be included in the Library. What you can try is to select each blue collection in turn and from the File menu choose "Exclude from Library" and then "Include in Library" right afterwards. That'll include ALL entries in the Library for sure.
To deal with duplicates afterwards, use the "Display Duplicates" command found under the View menu while you're in the Library. That'll show you all the duplicates and you can select them (use the Command key to select multiples) and delete them.
Or if you'd prefer for us to take a look at your database instead and fix it up as necessary, email it to us. You'll find our email on the
Support page. You'll find the database file in your Home folder under ~/Library/Application Support/DVDpedia/Database.dvdpd. Please archive the file before sending it to save space. (Select it and choose 'Archive' or 'Compress' from the File menu. That'll create a new file called 'Database.dvdpd.zip' which you can then attach to the email.)
If you don't see the ~/Library/ folder in Home you can use the Finder's 'Go' menu, hold down the Option key and the Library folder will appear.