Cliff's story about his brother James originates from Bill Cosby's actual life as brother James died of Rheumatic fever in 1947.
In "Cliff Babysits," we learn Cliff had a younger brother. James Theodore Huxtable died at the age of seven of rheumatic fever. Cliff was eight years old at the time.
At the beginning of the episode, the family without Cliff and Clair attend a Michael Jackson concert, and Jackson is on tour supporting his Bad album. However, the Huxtable family lived in Brooklyn, New York, but Michael performed in NYC on that tour was on March 3-5, 1988, at Madison Square Garden. This episode aired in January of 1989, so they could have attended one of his three shows in March of 88 at MSG for this episode's storyline.