Continuity mistake: When James Earl Jones puts his hat down on the piano, he puts it upside down. But in a later shot, as he tells Jack that he's fired, we can see the hat is now the right way up, behind Karen. Later it's upside down again.
Continuity mistake: When Karen asks James Earl Jones is she can ride on his shoulders, we can see James' hat sitting on top of the piano. In the next shot it is suddenly back in James' hands, and he then puts it down again.
Continuity mistake: When Jack is teaching James Earl Jones to act, we can see the table behind him has a script sitting on the middle of the table. When he goes to pick it up, the script is now sitting on the edge.