" the jewish arm" is usually the arm that is used for picking up a tab or leaving to tip a waitress. for example, Ira Goldberg is right handed and he and some friends are out to lunch, when the check comes, Ira suddenly cant move his right arm in order to reach in his pocket and get money. Thats the jewish arm.
There is also " the jewish ear" which is when someone tells Ira the cost and he claims he cant hear and tries to walk away. This is very common in the Hassidic community.