Homer: No. Wait a minute, what was that last one again?
Homer: (Recalling) Lisa, stop playing that stupid...saxophone! Yes, that's it!
Jerry: Alto or tenor?
Lisa: (on the phone) Dad, I broke my last saxophone reed, and I need you to get me a new one.
Homer: Uh, isn't this the kind of thing your mother's better at?
Lisa: I called her, she's not home. I also tried Mr. Flanders, Aunt Patty, Aunt Selma, Dr. Hibbert, Reverend Lovejoy, and that nice man who caught the snake in our basement.
Homer: Wow, and after them, out of all the people in the world, you chose me.
Pet Salesman: Oh my, what is that smell? Oh it's you.
Homer: 'Scuse me, do you sell ponies?
Pet Salesman: Uh…sure pal, right here.
Homer: Deer Hound...hey this is a dog!
Homer: I'll buy her that pony she's always bugging me for.
Marge: We can't afford to buy a pony.
Homer: Marge, with today's gasoline prices, we can't afford not to buy a pony.
Homer: Look, I let you down, and I apologize, I know that doesn't make it right, but I hope you can find it in your heart to forgive me.
Lisa: I forgive you.
Homer: D'oh! You didn't mean that!
When Homer first gets Lisa the horse he puts it in her bed, when she wakes up she opens the covers to the sight of the horse's head and screams just like the movie director's scene in the 1972 film.
The show Homer is watching, while Lisa makes her first steps, is Fantasy Island.
2001: A Space Odyssey
The scene with early man learning about fire & the wheel and "Homer" looking up at the obelisk is a reference to the opening scene of the 1968 film directed by Stanley Kubrick.
Millicent is modeled after actress Katharine Hepburn
All Creatures Great & Small
The pet shop is a spoof on the book title by the British veterinary surgeon Alf Wight, under the pseudonym James Herriot