Chad, here's my explanation.
I used Logic Pro's pitch editor to figure out what Greg was talking about. I had asked David his opinion and he said that when, for example on verse 1, Janice sings "a little fun" "a little FUN" "a little FUN" he hears the second and third "fun" as being a half step up from the first "fun." Well, of course that would be sharp and dissonant although he much liked the sound.
But this drove me nuts because I could not hear dissonance and I have a pretty good ear for pitch..not for melodies but for tuning, etc. So with the pitch editor I saw that the first fun was a C and the next two were C#. So he was right but I still didn't hear any dissonance. Janice just said she was following the piano as though I should understand what's happening in her head :) I pondered and pondered. Then it hit me.
So here's what I think is happening...during the "little fun" riffing the chord changes From a C7 to a C7b9 on the first verse line of and from a C7 to a A7b9 on the second verse line while she is doing the fun repeat. As mentioned in both lines the first "fun" is a C and the second and third are C# BUT a C# is a chord note in both the C7b9 and A7b9 and actually is the root note for the C7b7. So it wouldn't surprise me if she was hearing that from the piano and riffing off it. But if a C# is a root and/or chord note would singing it be dissonant? I say no and what they are reacting to is the change to the 7b9 chords.
I sent all this to David and he said "exactly" and was amazed that Janice could follow the piano to that degree. Me too.
A7b9: C# A C# E G A#
C7b9: C E G Bb Db
So that's my story and I'm sticking to it! Made me sound like Noel.