Continuity mistake: In the kitchen at the beginning when they are sitting at the table Fran says "Gracie when do you come up with these things." There is a note pad with a pencil on it in front of Grace. The shot changes and Fran is holding the pencil - the next shot Grace is now holding it.
Continuity mistake: When C.C. is trying to get Grace to play with the son of the Broadway critic she is coloring with a green crayon. Near the end of the scene it is suddenly a red one, and the paper she is coloring on is all red with no green so she could not have changed colors.