It should be "MERRY Christmas," not "HAPPY Christmas." However, we always say "Happy Thanksgiving," but we never say "Merry Thanksgiving." Do you ever hear anybody say "Merry Thanksgiving"? No. You only use Merry for Christmas. Merry Halloween just sounds weird.

It should be "We've no FEWER days....."

It should've been "We now don our gay apparel" or "Do we now don our gay apparel".

It is grammatically incorrect to say "The Lord IS come." It would be more grammaticaly correct to say "The Lord HAS come" or "The Lord is COMING." Nevertheless, that's the way the song was written. Why they wrote it that way is beyond me.

These two lines were meant to rhyme nicely, but even a child could tell you that the first line should be 'Mamie O'Rourke and I,' since the singer claims to be the agent of the action in question ('[tripping] the light fantastic').

It would need to say "and OF whom angels sing" to be grammatically correct, because "sing" as a transitive verb needs a song or songs as its object. One can't sing a person (including a saviour, king, or Messiah); one sings a song or songs, and that / those song(s) is or are the object of sing as a transitive verb. But it would be difficult or impossible to use "sing" correctly here as a transitive verb and fit the meter of the song. Incidentally, in what I've know as the old original version of this song, these lines are in only the first verse. That is the version I prefer (not necessarily on grammatical grounds). In modern adulterated versions of the song, these lines get repeated in subsequent verses, which doesn't fit "to a T" the context of those later verses. Worse still, the repetition gets boring.