Do I look Jewish?

In the 1997 Academy Award winning film, As Good As It Gets (see blog post), Melvin (Jack Nicholson) tells Carol the waitress (Helen Hunt), "There are Jews at my table."  How does he know that?  

The two actors (Peter Jacobson and Lisa Edelstein) cast as restaurant customers in this scene have stereo-typical Jewish faces.  But is it always so easy to identify who is a Jew?

Do these Jewish actors look Jewish?:  Jeff Chandler, Lee J. Cobb, Kirk Douglas, John Garfield, Paulette Goddard, Edward G. Robinson, Hedy Lamarr, Dinah Shore, Eli Wallach, Lauren Bacall, Tony Curtis, Peter Falk, Judy Holliday, Walter Matthau and Vic Morrow.

Do I look Jewish?  Let me tell you a story.

One day in the 1990s, my friend Joe and I left our office (Seagram's Tax Department) at 800 Third Avenue in Manhattan to go out for lunch.  I noticed a Lubavitch (Ultra-Orthodox Jewish movement) van parked on the street and a number of young Lubavitcher men walking around.  

As a secular Jew, I feared they would approach and try to pressure me to put on tallit and tefillin and return to the religion of my birth.  That was something I did not want to do.  Best to avoid them. 

Joe and I managed to do that on our way to the  restaurant.  However, after lunch while returning to our office, I noticed a young Lubavitcher man walking directly towards us.  There was no escape.  

I started to formulate my response.  Instead, he asked Joe, an Italian-American, “Are you Jewish?”  He of course answered no.  Then the young man walked away, ignoring me.

I was indignant.  I am Jewish, I said to myself.  How could he think Joe was Jewish?  How could he not know I was the Jew?

Or is it not always possible to identify who is a Jew by their face?