Orthodox Jews hold that your mother must be Jewish for you to be Jewish. I think this is also the official criterion in Israel when they determine who is Jewish.
The reformist and conservative wings of Judaism I believe say you can be Jewish if either your mother or father is Jewish.
Anyone can convert to Judaism and become Jewish religiously, but not ethnically. Kind of complicated, so I'm not sure where that leaves Mark. What is safe to say, as has already been mentioned, is that he is of Jewish decent or has Jewish roots. But how that qualifies him for "Jews in showbiz" is a bit strange.
