After some further sleuthing, I discovered that the culprit may go beyond simple spelling mistakes made by myself or others (I get CD info from CDDB). It appears that inconstancies between my info and Apple's, such as genre or year of release, may make a difference.
So the tip is, if you have an album that you know is available in the store, but you can't seem to get the art to download, adjust your settings in the song's Get Info (Command-I) panel. You can compare what Apple has by selecting the album in the music store and looking to the right of the cover image. The area around the cover image in the store has most of the information you might need to adjust -- Group, Album, Genre, Copyright/Release Year.

