Continuity mistake: When Bill and Chris Rock are singing on stage, during the line when Chris is saying "A voice as big as the sea" the camera fade cuts to a different angle while he's saying this line in what's supposed to be a live show. But his face and mouth are in very different positions between these fade cuts. And this happens several more times through the song with these fade cuts.
Continuity mistake: After Liz and Bev tell Bill that they can't cancel the show, they are helping him put his suit jacket on. Dimitri behind him is using a sticky roller thing to get hairs off the jacket and is down on his back. After Bev mentions the weather issues the camera angle changes and suddenly Dimitri has the roller up on his shoulder.