After gym signups, Lisa is shown wearing hockey gear, in reference to her previous stint as a goalie in Lisa on Ice.
Homer tells Mel Brooks that his movie Young Frankenstein "scared the hell out of him." In actuality, Young Frankenstein (like most Mel Brooks movies) is a comedy, which explains Brooks's less than enthusiastic response to Homer's comment.
Bart's ballet teacher tells him to "leap like he's never been before" is a reference to the 1987 Simpson short, "Jumping Bart", where Homer tells him the same thing.
Barney smokes a cigar without removing the wrapper and sees "Sgt. Pepper" (a reference to the album of The Beatles: "Sgt. Pepper's Lonely Hearts Club Band") growing out of Homer's back.