I thought I might get the answer to this question before she died, but no luck.  So, is Carol supposed to be a bad singer?  In the George/York  then York/Emily scene, it looks like York and George wince, which might be unrelated, and there's very little applause.  The record version is mixed a little differently, and while it may be the same performer, I don't think it's the same performance.  Was this just an unmentioned subtlety in a very unsubtle game, or was this unplanned?

I WANT to say they planned it. I really do.

" I WANT to say they planned it. I really do. "

Spoilers?

Here's Carol singing (with George and York maybe / maybe not reacting): 
  

the recorded version sounds slightly better

Well the reason it sounds bad is because it's a Japanese woman singing the song phonetically.  The Amazing Grace song is the same way, as well. 

No, it's a Japanese game so any joke would've bin overdone to the point that it stops being funny. See: Emily's cooking.

I don't think those glances are referring to the song. I think George is just looking away because he's feeling (or pretending to feel?) guilty about the girl's deaths, which leads to his big speech to York in the next scene.
 
I love Carol's Engrish though. If they decided to hire a whole English-speaking cast, I don't get why they couldn't have done the same for their singers.

I have tried a few times to decipher the lyrics.  I wondered if anyone had a better guess about these-
 
 i dream of {fear?}, like {something}, you are conscious of my innocence, everyone's just {something something}, life is but a dream
i dream of you, like a god, there is something funny about this song, wait behind the door of leaves {or possibly 'please'}, they should see us, i {something} from the night, {my space?}
 
There's a cover that someone did on youtube that's kinda... off in the same way that the original is off, except its...  well, its Thomas's version.
 http://www.youtube.com/watch?v=Osur5lo4Q2U his guesses are a little different from mine, I guess.

  @100_Hertz: Yes, all the voice acting was, but it's pretty clear listening to the songs that they were sung by someone whose primary language is not English.  Looking at the credits, the vocals for Carol's song and Greenvale were sung by Misako Yamashita, and Amazing Grace was sung by REMI.