Continuity mistake: When Doris is watching The Fat Albert Show, she is holding the remote out just above her knee. When her tear falls down, it falls directly in the middle of the remote.
Continuity mistake: When Bill Cosby (appearing as himself) opens his door to find Fat Albert there, Fat Albert puts his hand out to shake Cosby's. In the next shot, he puts his hand out again.
Continuity mistake: At the track meet, Laurie runs the third leg of the 4x100 and hands off to Doris to run the anchor leg. At the finish line, Laurie is there to cheer on Doris as she crosses line first. Only the first and second runners of this relay would have time to make it to the finish line in time to see the end of the race.
Continuity mistake: In the live action shots, Fat Albert always has a belt. In almost all of the cartoon shots, he doesn't have a belt, though he does in a few cartoon shots. The director admits to this mistake in the commentary, though he apparently only noticed it in one shot.
Answer: He has said in many interviews that they were based on his friends growing up. The characters of Bill and his little brother Russell, were Bill Cosby and his brother Russell. Thou the adventures were exaggerated, the characterizations were real.