Even though it's supposed to just be a joke, Jesse wouldn't have been able to vote in more than two presidential elections at this point much less for three past presidents. The earliest he could have voted for a president would have been 1984 since he turned 18 in 1981.
5 years earlier, Edie McClurg was playing Mrs. Poole on the sitcom Valerie (The Hogan Family). In the episode 'Boston Tea Party (January 4, 1987), Jodie Sweeten played Mrs. Poole's niece Pamela.
Joey has a poster in his room that is the same poster Joey and Chandler have in their apartment in Friends. It's a poster of Laurel and Hardy.
Jesse and Joey are now DJs at the radio station now that Joey has quit The Ranger Joe Show after his new obnoxious co-host Jungle Jenny humiliated him.