Jazz drives a 1964 Impala
Will makes a comment to Aunt Viv that he "got in one little fight and my mom got scared." This is a line from the original series opening and song by Will Smith.
In the extended version of The Fresh Prince of Bel-Air theme song Will sings "First class, yo this is bad! Drinking Orange Juice out of a Champagne glass!" On Will's flight in this episode of Bel-Air, Will has a glass of orange juice in a champagne glass.
This isn't the first time the character of Carlton Banks takes drugs. In the original sitcom version, Carlton takes drugs in the first season, albeit by accident partly due to a burned out Will.
Toward the beginning, when Will is in class in Philly, the teacher makes a comment to Wills friend Trey. This could be a reference to Don Cheadle's character in the original sitcom Ice Trey. Episode titled Homeboy, Sweet Homeboy