Thanks for the responses. Indeed, in the (massive) full music listing I can see ALL playlists it is in.
Part of the problem is that you don't always know what playlist you are playing if you have been editing or moving around the library, hence a full list of all playlists would be better, by probably not critical for a player.
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As for management capability, iTunes is functionally light compared to other music management apps. I had typed a very long list of issues, but they're not your problems and you have been very helpful with the 'show in playlist' issue.
But as you asked, in short, with iTunes you can't sync playlists with non-Apple devices (most notably the flashdisks in my new car), can't play 20% of my tunes (FLAC, WMA, OGG, etc.), can't import songs into playlists with some foreign characters (even though it let them into the library), can't manage the music folders/location on the harddisk making workflows for adding large numbers of tunes for fixing very problematic, can't export multiple playlists, each M3U files need editing before importing into other media player, can't standardize views for all playlists, hard to identify songs needing fixing (artwork, artist name, album details, etc.), can't customize blue-gray look and feel, there is no 'now playing' window showing the tunes queued so can't create mixes on the fly, album art searching limited to iTunes shop with no ability to edit query (exact match or fail), can't sort songs on file/folder location, can't easily jump from a song to view all by the artist or rest of album, no lyrics window, no lyrics searching tool, no community of app/script developers to fill out functionality, can barely see what is now playing in top window giving the song title and artist (a 5 point font I suspect), can't see next songs queued to play (or add songs to be played on the fly), etc.
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I now realize that you
have to use iTunes or nothing works on a Mac (no iMovie, no iPhoto, no FrontRow, etc.). I struggled for months managing my music through a Win7 VM app, but I admit defeat (although I still need the Win7 music app to sync my weekly podcasts 'cos iTunes can't). So I trade-off openness & functionality for being able to do basic home computing - trading not being able to sync music to devices or easily add & fix large numbers of music files, for being able to use iMovies, Aperture, FrontRow, etc. I'll add small numbers of songs for the kids, but my growing 3,000+ waiting-list songs will have to wait even longer. I just wish iTunes had a big brother like iPhoto has Aperture, or iMovie has FinalCut. Unless there are plans for an iTunes+ in the pipeline???
Sorry for the long moan, thanks again for your quick and helpful responses.