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1. Make a smart playlist called “All Files” with this rule: “Artist” is not “123456789″ (or any nonsense name that won’t be in your library).
2. Make a static playlist called “All Live Files”.
3. Make a smart playlist called “Missing Files” with these rules: Match all of the following rules, Playlist is “All Files”, Playlist is not “All Live Files”
4. Select all the files from “All Files” and drag them into “All Live Files”. The dead files marked (!) will not copy over.
5. “Missing Files” will contain all of your dead files. Select all and delete. Voila, a nice clean iTunes library.
The trap is that you can't just select and delete from smart playlists in recent versions of iTunes. You need to hold down the Option key on a Mac while pressing Delete, or use Shift + Delete on Windows.