It's one of the more heart-warming performances of the number -- which is saying a lot, since anytime Kermit sings "The Rainbow Connection," it's pretty heart-warming. But this time, things were ratcheted up a bit because halfway through the number, Paul Willams himself came on stage to join him in a duet.
The other Muppets popped in later, as well. (By the way, the bearded-human who comes on stage towards to end to participate, is Bobby Moynihan, formerly of SNL, who was the evening's host.)
One small thing occurred to me with Kermit's introduction. I've heard him sing the song countless times, and I don't recall hearing him ever credit the song's writers, as he does here. I have a feeling that's to give a sort of advance notice to the audience so that they'd know it's Paul Williams when he walks out on stage, if they're from a few recent generation who doesn't recognize the singer.
This is a rough video posted on YouTube, but you still get a pretty good version of it all. A lovely performance all around.