1. Round yon virgin
The "round" in "Silent Night" might call up imagery of the soft, maternal kind, but in the phrase "round yon virgin," it simply means "around." "Yon" is an antiquated word for "that one" or "over there." The meaning of the phrase in the song depends on the line before it. It should be understood in the context "all is calm, all is bright round yon virgin mother and child." In other words "Everything is calm and bright around that virgin mother over there and her child." In technical terms, "round yon virgin mother and child" is a prepositional phrase.
2. Troll the ancient yuletide carol
Trolling a carol might sound like some obnoxious attempt to undermine it, but it's actually a great way to get in the holiday spirit. According to the OED, one of the meanings of "troll," in use since the 16th century, is "to sing in a full, rolling voice; to chant merrily or jovially." It's related to the sense of rolling, or passing around, and probably came to be used to mean singing because of rounds, where the melody is passed from one person to the next. The modern, obnoxious sense of troll comes from a much later importation from Scandinavian mythology. People have increasingly been changing this line to "toll the ancient Yuletide carol" (now over 17,000 hits on Google). Don't let the trolls win! Let's troll the trolls by dragging this word back to the cheery side!
3. The little Lord Jesus laid down his sweet head
"Away in a manger, no crib for a bed / The little Lord Jesus laid down his sweet head." This line is a perfect storm of lay/lie confusion. The correct form here is "laid," but it often gets changed to "lay," and with good reason. "Laid" is the past tense of "lay," which should be used here because the little Lord Jesus isn't simply reposing (lying), but setting something down (laying), namely, his head.
If it were in the present tense, you could say he "lays down his sweet head." But in the past tense "lay" is the form for "lie." I know. It's a rule that seems rigged just to trip people up. But here, it gets even worse, because the word right after "laid" is "down." There's a word ending with 'd' followed by a word beginning with 'd.' When you say "laid down," it's hard to tell whether that first 'd' is there or not. As a practical matter, both "lay" and "laid" sound exactly the same in this context. So you can fudge it when you sing it. Just be careful how you write it.
4. You better watch out, you better not cry
That's right, Santa Claus is coming to town, so you better watch out. Or is it "you'd better watch out?" Many grammar guides advise that the proper form is "you'd better" because the construction comes from "you had better," and it doesn't make sense without the "had." The problem is, it doesn't make much sense with the "had" either, if you want to do a picky word-by-word breakdown.
Though the "had better" construction has been a part of English for 1000 years, it came from a distortion of phrases like "him were better that he never were born," where "were" was a subjunctive ("it would have been better") and "him" (or "me," "you," "us") was in the dative case ("him were better" = "it would have been better for him"). People started changing the dative to the subject case ("he were better") and then changed the "were" to "had."
That was all hundreds of years ago. Then, in the 1800s, people started dropping the "had." The grammar books of the late 1800s tried mightily to shore up the "had" (some even making up a rule from nowhere that it should be "would," as in "he would better"), but these days the bare form is considered correct, if a bit casual for formal contexts. Clearly, "Santa Claus is Coming to Town" wants nothing to do with fancy formality. So "you better watch out" is the way to go.
5. With the kids jingle belling and mistletoeing
There is a lot of verbing going on in "It's the Most Wonderful Time of the Year." First, "With the kids jingle belling/And everyone telling you 'Be of good cheer'," and then, "There'll be much mistletoeing/And hearts will be glowing when loved ones are near." Of course, in a song, concessions to rhythm and rhyme need to be made, and sometimes this involves making up a few words. But the practice of turning nouns into verbs is as old as English itself. Many of our verbs started when someone decided to use a noun to stand for some verbal notion related to that noun. First we had "hammer," and from that we made "hammering." First we had "message," and now we have "messaging." Oil, oiling, sled, sledding, battle, battling. The meaning of the verb is built off some context involving the noun, which could be almost anything (pounding with a hammer, sending a message, putting oil on, riding a sled, engaging in a battle). So verbs for "ringing jingle bells" or "kissing under the mistletoe" aren't so strange at all. At least no more strange than "gifting" or "dialoguing."
6. God rest you merry, gentlemen
Notice the comma placement there? The gentlemen in this phrase are not necessarily taken to be merry already. It's not "Hey, you! You merry gentlemen! God rest you!" It's "Hey, you gentlemen over there! May God rest you merry!"
In Shakespeare's time, "rest you merry" was a way to express good wishes, to say something like "peace and happiness to you." Other versions were "rest you fair" or "rest you happy." It came from a sense of "rest" meaning "be at ease," which we still use in the phrase "rest assured." In "God rest you merry," "you" is the object of "rest," so when people make the song sound more old-timey by substituting "ye" for "you," they are messing up the original grammar because "ye" was the subject form.
Actually, that's not quite true, because even in Shakespeare's time, "ye" was sometimes used as the object form. However, if you want to go that way, you should be consistent with your pronouns and sing "God rest ye merry gentlemen/Let nothing ye dismay." In the second line "you" is also an object, as in "Let nothing dismay you."
So rest you merry this season, and enjoy your jingle belling, mistletoeing, and trolling.