When the feds came with a search warrant to comb over the Hill residence in Goodfellas (and get the wheels greased), Karen allows them in a blasé manner, and resigns herself to watch TV with her children.
We see she is watching Al Jolson in The Jazz Singer:
Scorsese doesn't so much as breathe on set without having a good reason. Why did he choose this program? Is Karen hearkening to a simpler time? She was born in the mid-40's. (too late to have lived in an era where this a part of her upbringing) Surely there must be a purpose or statement that Scorsese put this in the film.