Wow, I've had "Right Where I Belong" on my mind quite a bit lately, because I got a few more things I've noticed....
Kermit sings the song in the dressing room right before they go on stage and sing it, but by then there's a bit of a change in the lyrics. There's an entire verse changed. In the dressing room, he sings "I see that old face coming back to me like an old familiar song....", which is more appropriate for the scene (since Kermit has just gotten his memory back AND he's reunited with most of his friends), while on stage they sing "the curtain's up and the lights are bright and they're playing our old song..." Also, on stage the last verse ends a little sooner than it did backstage. Maybe Kermit decided on these changes just before they go on stage, or somebody did make the changes and Kermit was informed of the change before the curtain raised.
When they come across all their friends who are backstage, why are Bill, Gil, and Jill there? All the others came with the main characters as they traveled, but I don't know why those three would be there. The others didn't exactly befriend them while trying to cure Kermit's amnesia. Could they have decided, after Kermit was taken away, to inform Pete that some of his staff stole him and he explained things to them? Could they have just paid attention to the fact that they mentioned something about him doing a show that night (though they didn't say the title or theater... though again, they could have talked with Pete or Rizzo or someone and given the details, or maybe, with the mention of a show opening that night, Manhattan Melodies might have been the only show opening that night).
It's interesting that the rats were not among the friends backstage who Kermit decided to let on stage (unless maybe they were behind some characters or it's a rare case of them actually putting them to proper scale with the others, preventing them from being seen by the camera), though they do appear in the play.
And does Kermit, as just the shows star and writer, have the authority to just let all his friends appear in the play on such short notice? Wouldn't he need to talk with Ronnie or Bernard Crawford on the subject (though I can see Ronnie being okay with it)?
With the running gag of Kermit starting to sing the song only to be interrupted, it would have been appropriate if that was the song he sang before getting hit by a car, instead of Together Again (though in this case singing that song is a bit more appropriate since he's expecting to see his friends again soon). Like, Kermit could have sung as far as he had at other points only to be interrupted by a car instead of somebody stopping him from singing.