Library shows duplicate songs but are same file
Bear in mind this is true of only two songs out of 37 on my playlist.
How do I get rid of the extra entry?
There is a difference between duplicate music files and duplicate library entries.
Have you re-organised your music files? Have you run the evil "Consolidate Music Library" command? Or added directories to the library after reorganisation?
I've had similar problems and I've deleted the library and had iTunes rebuild the library. Sure, you lose some library specific data. It also depends on all your music being contained in a single directory (plus sub directories). Long ago, I learnt the lesson of letting iTunes organising my music and copying any music it played via double-clicking to the iTunes music directory.