Cover Art Downloader reads from the Android media database, so it will show all the albums that your music player does with the exception of music stored on internal memory because market applications cannot access media stored in internal memory.
If albums are failing to show up that are stored on the sd card, it would be because either:
1) You have recently downloaded the music directly to the phone, and it does not currently exist in Androids database. Cover Art Downloader has a built-in media scanner for this purpose, just press the Menu button then press Media Scanner.
2) The albums are missing all or some of their id3 tags. This happens when you use certain mp3 searching applications that remove album tags to prevent detection of illegally distributed music. To fix this, you will need to export the music to your computer and fix the tags. I recommend Musicbrainz Picard for this task.
3) The current market version of Cover Art Downloader (1.2.9) has a bug where it will not show albums where the title is the same as an album by another artist, such as a "Greatest Hits" album. This will be fixed in the next version due out soon.
You can try other grabbers if you like, but none match the speed, simplicity, features or match rate of Cover Art Downloader, and they will all have the same limitations regarding music stored internally, music not yet scanned by Android and music with missing or incorrect tags.
If you are rooted you can use a file manager (astro, es, root explorer, etc) to move the files directly, without root though they face the same problem as all other market apps in that it cannot read the files from internal memory and you will get 'Copy failed'.
Without root you will need to connect the phone to your computer and move the files from the internal storage drive to the external storage drive.