Okay, I give up. How do I delete a track from within a Smart Playlist
in iTunes? I can delete them from the Library folder, but I've got a
smart playlist that finds files with a play-count of one or more OR
have a star rating of one.  I want to delete those easily.

Secondly, is there a way for iTunes to automatically delete tracks
that fit a certain criteria -- i.e. If I mark a track with one star,
can it be automatically deleted once it syncs? I know I can create a
smart playlist that only shows the 1-stars, but is there any way to
have it automatically delete those?

I don't think you can do either of those things using iTunes alone.
You may be able to write a script (using AppleScript on a Mac or the
iTunes SDK on a PC), but that's probably more effort than it's worth,
especially if you don't have any experience with
scripting/programming.