Joey's joke in the beginning about "Mr. Ed Meese" refers to the Wedtech scandal which involved government contracts. Edwin Meese was Attorney General of the United States at the time and was charged with complicity in the scandal. He would later resign in August 1988, six months after this episode aired. Several people Meese was connected to ended up going to prison as Joey's joke references.
Joey catches DJ watching Late Night with David Letterman, which, at the time, ran from 9:30-10:30 pm PST. DJ tells Joey that Stephanie slept through The Tonight Show, Starring Johnny Carson, which, also at the time, ran from 8:30-9:30 pm PST.