When Homer says, "That shot is impossible! Jack Nicholson himself couldn't make it!", he is thinking of Jack Nicklaus, a retired American professional golfer considered to be one of the greatest of all time.
When Homer tells Bart that his putter's name is "Charlene", it is a reference to a scene in Full Metal Jacket where Marines in basic training are ordered to give their rifles female names. Leonard "Gomer Pyle" Lawrence names his "Charlene".
When Lisa finds "Golf" at the card catalog, one of the topics it contained was "Eisenhower". Dwight D. Eisenhower played golf frequently during and after his presidency and was unreserved in expressing his passion for the game.
Lisa borrows Tao Te Ching by Laozi from the library. The Tao Te Ching is a fundamental text for both philosophical and religious Taoism.
Bart assumes a "crane stance" in the backyard, similar to Daniel LaRusso in The Karate Kid
While Bart is being trained in golf by Lisa, at one point he assumes a "crane stance" in the backyard, similar to Daniel LaRusso in The Karate Kid.
Homer was reading the comic strip Marmaduke on the newspaper.
When the family is having breakfast, Lisa makes a reference to the Kentucky Derby.
The phrase that Flanders says, "Mercy is for the weak, Todd!" is a reference to a line said by the antagonist John Kreese in the 1984 film The Karate Kid.
Homer cites American football coach Vince Lombardi. Lombardi is considered by many to be the greatest coach in football history.
The British announcer thinks Bart and Todd's decision to end the game in a draw is "the most stirring display of gallantry and sportsmanship since Mountbatten gave Egypt back to the Punjabis" Lord Mountbatten, uncle of Queen Elizabeth II's husband Prince Philip, being Viceroy of India during partition of India in 1947. The closed captions on the DVD have India as Egypt.
This is the first episode to feature the Flanders family prominently. His phone conversation with Lovejoy, who is even on speed dial at the Flanders household, also introduces us to Ned's staunchly Christian views.