The idea that there is a carnal/spiritual duality is alien to Jewish thought it is a christian-greek pagan thing. Sex is not prohibited on the sabbath it is a mitzvah. Mr. Cohen is very Jewish http://youtu.be/4imJ7wWB9FU here he is giving the priestly blessing. I think Scotty Moorhead stumbled at the verse only understanding the sex part. As a Jew like Leonard I will have to differ on the Christian reference the word Hallelujah contains a name of the God of Israel.

You say that I profane the name

The final syllable is the first two letters of the holy name YHVH. So the haredim could get all snotty and accuse our favorite Kohen of being impious for putting the name of God in a naughty song.

no one even knows the name

The thing is that the pronunciation is not know at least traditionally.[ Yaweh is prolly the right one.]

and if I did then whats it to ya,

coolest line ever

there is a blaze of light in every word

straight out of the Zohar. [a book of jewish mystism]

It doesn't matter which you heard The holy or the broken Hallelujah

here you could get christian if you wanted there is some parallel with peters vision of the net. but Cohen is still paraphrasing the Zohar. There is another more secret name of God that includes all 22 letter making every word contain a part of the name of God. It makes every utterance sacred even the screams of oh God during sex.

I think the song is akin to the two faces or a vase pictures. It is a song about lost love and sex and a song about God. the tradition is very old remember Shlomo wrote

I have taken off my robe - must I put it on again? I have washed my feet - must I soil them again? My lover thrust his hand through the latch-opening; my heart began to pound for him. I arose to open for my lover, and my hands dripped with myrrh., on the handles of the lock.

And that is about God right? it is in the bible. :)