The song has appeared two times in Lost:
- "The Long Con" – Hurley and Sayid were trying to find a signal on the Arrow radio, and instead found a radio broadcast which was playing the song. Sayid mentioned that the radio could be picking up signals from anywhere in the world. Hurley cleverly responds, "Or any time. Just kidding, dude."
- "A Tale of Two Cities" – Jack heard it on his car radio while he watched Sarah with her new man.
- In The Twilight Zone episode "Static", an old man picks ups a live radio signal from 20 years in the past, a DJ introducing this song. He also picks up other broadcasts from the 30's and 40's. However only the old man can hear the song, while other characters only perceive static. He attempts to correct mistakes he has made in his life using this knowledge. This could be the basis for Hurley's humorous quip. 
- Glenn Miller disappeared on December 15, 1944, en route from England to Paris to play for troops in the recently liberated city. Neither his remains nor the aircraft in which he was riding were ever found.
I stand at your gate and the song that I sing is of moonlight.
The stars are aglow and tonight how their light sets me dreaming.
Let us stray till break of day
So don't let me wait, come to me tenderly in the June night.
- Wikipedia - "Moonlight Serenade"