Not much, apparently.
In this 2004 interview with Deidre Bair, author of the best and most thorough biography of Jung (Jung — A Biography), Charlie Rose clearly lacks much knowledge about Jung and has no perspective of his importance in the current culture.
Click to go to interview: http://www.charlierose.com/view/interview/1323
I would also note that Ms. Bair is given only 10 minutes (Hollywood actors often get an hour) to convey the history and thinking of Jung – kind of a fast foot approach to philosophy and psychology.
It is surprising to me that a man of Rose’s intellect (and someone associated with Bill Moyers) who clearly has a wide-range of interestes has so little understanding or interest in Jung. (I would note that his training is as an attorney, so he already has a bit of a biased, external viewpoint.) I think his attitude also reflects the view of the extroverted culture in general, which associates psychology and dreams with Freud and finds little of value in the internal life.
Mr. Rose has been through a divorce, a failed long term relationship, and major heart surgery. Knowledge about Jung’s theories would have helped in all of these situations.
Charlie had another chance when the Red Book came out, but as far as I can tell he gave no interviews related to this watershed event. He has another chance on July 26, 2011, the 50th anniversary of Jung’s death.