The chalkboard gag reads "I am not the Sixth Beatle", a reference to the 'Fifth Beatle'.
One of the Thanksgiving parade balloons is of Rusty the Clown, a reference to Rusty Nails, who was a popular TV clown in 1960's Portland, Oregon, where Simpsons creator Matt Groening grew up, and on whom Krusty the Clown is loosely based.
When Smithers is telling Mr. Burns that he's going to be gone for a while due to being nominated for a starring role of a Malibu Stacy musical he penned, Mr. Burns then proceeds to use a novelty gun with a flag that pops out on Smithers to show him what he discovered, only to press it again when irritated that it didn't shoot out before the flag flies into Smither's chest, mirroring one of the signature weapons of Batman's nemesis, The Joker, in the Batman comics.
The gulls trying to eat the people with fish guts is a reference to The Birds.
When the family are about to head out the door, Lisa's underwear is briefly seen under her dress.
The "panda rape" scene was very controversial among fans of the show, with most citing it as a sign that the show has devolved into vulgar South Park/Family Guy-style humor to stay relevant.
The panda rape scene—along with evidence that most of the story elements from this episode have been recycled from previous episodes [The Simpsons have money issues, Homer becomes Smithers' replacement when Smithers takes a sabbatical from work, Lisa worries over someone selling their soul and moralistic issues, Homer dresses up as Santa Claus etc.] -- have been used as reasons why this episode is considered one of the worst in the series.
Homer throws a dish of pudding at Lenny (reluctantly, under Burns' persuasion).
Homer throws a dish of pudding at Carl (spontaneously, and Burns quickly reprimands him for it).
Homer buys a mint condition Spider-Man #1 from Comic Book Guy for $20,000 cash, then tears out the pages and eats it right there in the store, while Comic Book Guy gasps and collapses in shock.
Wearing only a giant diaper, Homer appears in the men's room at Springfield Stadium, acting like a baby needing a diaper change and saying: "Baby made a boom-boom!" in front of several disgusted men and a duchess.
Homer disguises himself as "Sim-Sim," the new female panda at the Springfield Zoo. The prank backfires when the zoo's trainers zap him with electrical prods and the resident bull panda, Ping-Ping, takes an amorous interest in him.
Burns offers Homer a million dollars to throw fish guts (instead of presents) to the crowd at the Thanksgiving Day parade. Homer refuses and Burns does it himself.
Recycled animation: During their Mariachi performance, the Simpsons are seen playing "La Bamba" (an up-tempo song) and "Spanish Eyes" (a slow song). The movements of them playing their instruments match "La Bamba" but not "Spanish Eyes"; the discrepancy is most obvious with Maggie's trumpet playing.