Theo comments that he's old enough to go into the service and that Cliff has been waiting for a monumental screw-up to give him a reason to make Theo enlist. A year later during the season five episode "Lost Weekend", Cliff would try enlisting Theo in the service.
Kim says that she does not have any sisters. But in a later episode Rudy says that Kim went to see a horror movie with her older sister.
Theo: (About he and Vanessa) You want us to wait in the car?
Cliff: Wait UNDER the car.
Theo: (To Vanessa) You know, I've always known you were boy crazy. And you know, I knew one day it would get me into trouble.
Rudy establishes that the Huxtables' address is 10 Stigwood Avenue.