Continuity Nod: This isn't the first time Bart was mad at Santa's Little Helper.
Epic Fail: When Homer tries to build a pigeon coop for Bart's bird, it's so rickety that when he merely pats it, rather then collapse into a pile, the staples pop out, causing the chicken wire to refold itself as the framework falls apart, then it rolls back into its box which is then resealed by the popped out staples. Yeah, it's one of Homer's specialEpic Fails.
Missing Mom: Nelson's mother runs off with the clown from his birthday party. She eventually returned, with the clown as her new husband.
Mocking Music: After the funeral for his pigeon, Bart's friends try to cheer him up with the song "Put On A Happy Face". It works...until Martin reveals it's from Bye Bye Birdie.
Mouse Hole: In the intro, when the Simpsons entered their living room, Prof. Frink shrunk them and they ran into the hole to escape the cat, only to end up on a Mouse Trap.
Rhetorical Question Blunder: At some point in the past, Santa's Little Helper dragged Bart around and a newspaper published it with the question "Who's walking who?". Homer says he sent the answer but they refused to publish it.
Strolling Through the Chaos: While Bart is being attacked by the ostrich, Marge and Lisa are unaware of what's happening while in the gift shop.
Shout-Out: The Itchy and Scratchy cartoon features several. The title (Dogday Hellody of 1933) is a play on Broadway Melody. The basic plot is a parody of Pluto's Judgement Day, while the parade of celebrity cameos brings (Including Harpo Marx, Will Rogers, and Edward G. Robinson) is reminiscent of the "Hollywood Party" style of Looney Tunes cartoons, such as Hollywood Steps Out
What the Hell, Hero?: Lisa becomes angry with Bart when he forces the family to leave Santa's Little Helper at the ostrich farm.