The two I remember were:
(1) If someone tells you they are going to “the city,” where are they going?
(2) Name a freeway.
The other TAs and I compiled the results. For (1), the northern Californians almost always answered “to San Francisco,” while the southern Californians gave a variety of answers, including “Huh?” For (2), the northerners gave a number, like “the 101,” while the southerners usually answered with a name, like “the Golden State” or “the Harbor Freeway.” (I haven’t been to California for a while, but my impression is that SoCal usage has shifted since the 1970s to numbers, too.)
The instructor of that class was Marc Okrand, who later created the Klingon language.