I went to City first.... In fact, the recording of "Goodnight Sweetheart" does not sync with the recording on my two precious 16mm film prints of the episode as originally broadcast. The voice is different as well as the arrangement of music. It seems to match the "restored" copy by the Sci-Fi channel, but it is NOT the original broadcast version. The original broadcast as aired had Rudy Vallée singing taken from the soundtrack of The Palm Beach Story
(1942). At some point in 1983 or so when the distribution of Trek moved to videotape, the original vanished and I presume an alternate recording was used...perhaps they recorded another version at the scoring session but liked the vintage sound of the movie soundtrack? I recall seeing it in syndication with no voice at all in the 90's. And, of course, they replaced the song all together as well as other incidental music on the Laserdisc and some VHS/Beta copies in the 80's. Curiously, I have a VHS from 1985 that has the same version as used by the Sci-Fi Channel. Paramount no longer owns the rights to this movie so I don't guess we'll be seeing the original broadcast version on any official release.