“Silent Night,” because of the flow of the tune, is often sung incorrectly, or at least thoughtlessly, in several ways. In the first verse, the tune encourages the singer to mentally punctuate the song thus:
Silent night, holy night.
All is calm, all is bright.
Round yon virgin, mother and child,
holy infant so tender and mild.
Sleep in heavenly peace! Sleep in heavenly peace!
Thinking of the text in two long lines here helps us to grasp the message of the stanza:
Silent night, holy night, all is calm, all is bright round yon virgin mother and Child.
Holy Infant, so tender and mild, sleep in heavenly peace, sleep in heavenly peace.
See the difference? I suspect we tend to mentally begin a new sentence with “round yon virgin” (as in the first example), which is not consistent with the text. As well, the phrase, “round yon virgin mother and Child” can lend itself to being sung, “round yon virgin, mother and Child,” which of course is not the point. To help vocally punctuate the song correctly, consider a break after “all is calm” and singing through without a breath the phrase “all is bright round yon virgin mother and child.” As well, perhaps it would be helpful to sing through without a breath “Holy Infant, so tender and mild, sleep in heavenly peace”.
In the third verse (“Silent night, holy night, Son of God, love’s pure light Radiant beams from thy holy face, With the dawn of redeeming grace, Jesus, Lord, at thy birth, Jesus, Lord, at thy birth.”), the adjective “radiant” modifies “love’s pure light,” not “beams,” and “beams” is a verb, not a noun. The phrase is, “Son of God, love’s pure light radiant beams from Thy holy face.” Additionally, the Son of God is being addressed, not equated with “love’s pure light.” Grammatically, the light is radiant, and it is beaming from the face of the Holy Child. “Son of God [vocative], love’s pure light [subject] radiant [adjective] beams [verb] from Thy holy face [adverbial phrase modifying “beams”].” I find it helpful here to avoid a breath or vocal break between “love’s pure light” and “radiant.”
Jubilate Deo 
Interesting. This actually occurred to me the other day when I was working on a setting of “Silent Night” with my adult choir. There are probably a number of texts, most we know well, that we sing incorrectly and, thus, do not interpret well.
Blessings
I wonder what the grammatical structure of the original German is; this is, after all, a translated work.
True enough. I’m afraid I haven’t learned German yet, so I can’t speak to the grammar of the German original. However, it does appear that the commonly-used English version of “Silent Night” takes some liberties with the original German text, if this analysis is accurate: http://german.about.com/library/blstillenachtB.htm.
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