The film revolves around, among other things, college football and a game between the fictional Darwin and Huxley Colleges. (Huxley was a defender of Charles Darwin's theory of evolution.) Many of the jokes about the amateur status of collegiate football players and how eligibility rules are stretched by collegiate athletic departments remain remarkably current. Groucho plays Quincy Adams Wagstaff, the president of Huxley College, and Zeppo is his son Frank, who convinces his father to recruit professional football players to boost the Huxley team's chance of winning. There are also many references to Prohibition. Baravelli (Chico) is an "iceman", who delivers ice and bootleg liquor from a local speakeasy. Pinky (Harpo, wearing his usual pink-colored "fright wig") is also an "iceman", as well as a part-time dogcatcher. Through a series of misunderstandings, Baravelli and Pinky are recruited to play on Huxley's football team; this requires them to enroll as students at Huxley, which, of course, results in nothing but comic chaos throughout the school. The climax of the movie, often referenced as one of the greatest football-related scenes in movie history , includes the four protagonists winning the football game by taking the ball into the end zone in a horse-drawn garbage wagon that resembles a chariot and which Pinky rides as such.
One famous scene features Baravelli guarding the speakeasy, and Wagstaff trying to get in. The password for entry is "Swordfish". This bit was the inspiration for the title of the movie thriller Swordfish. The sketch includes several jokes about fish, with some puns-within-puns:
During this scene, the mute character Pinky wants to come in and is asked the password; he responds by pulling a fish with a small sword stuck down its throat from his coat. At one point Wagstaff and Baravelli are debating the cost of ice. Wagstaff argues that his bill should be much smaller than it is:
The joke immediately after that one illustrates that the Hays Office was not in total control of film scripts yet, and hints at Chico's real-life lifestyle. The essence of this joke would be repeated by Chico in Duck Soup:
A notable scene taken from Fun in Hi Skule consists of the brothers disrupting an anatomy class. In this scene, the part of the anatomy professor is played by Robert Greig, a character actor who appeared in over 100 films, many in the role of a butler. He appeared with the Marx Brothers as Hives, the butler, in Animal Crackers. After Chico and Harpo "bear him out", Groucho takes over the class and continues the lecture:
Earlier in the scene, he recited this little poem in response to the professor asking the students to explain the symptoms of cirrhosis, which Baravelli mis-hears as "so roses":
A little later, Wagstaff advises Pinky that he "can't burn the candle at both ends". Pinky then reaches into his trenchcoat, and pulls out a candle burning at both ends.
The film prominently features the song "Everyone Says I Love You", by Bert Kalmar and Harry Ruby, which was later the title song of the eponymous 1996 Woody Allen movie Everyone Says I Love You. All four brothers perform the song:
Zeppo leads off with a "straight" verse, befitting his usual non-comical characterization:
Harpo whistles it to his horse, and later plays it on the harp. In keeping with his standard mute characterization, he does not sing it.
Chico sings a comical verse, with his standard fake Italian accent, while playing piano:
Groucho sings a somewhat sarcastic verse while strumming a guitar, befitting his attitude throughout the film of being suspicious about the college widow's intentions:
Except when Harpo (the dogcatcher) whistles it to his horse, the song is used to serenade Connie Bailey (played by Thelma Todd).
Eventually, Pinky and Baravelli are sent to kidnap two of the rival college's star players to prevent them from playing in the big game. The intended victims (who are much larger men than Pinky and Baravelli) manage to kidnap the pair instead, removing their outer clothing and locking them in a room. In order to escape, Pinky and Baravelli saw their way out through the floor. The saws came from a tool bag Pinky carried with them that held their "kidnappers' tools," which included, among other things, rope, chisels, hammers and at one point, a small pig. This is an example of the surreal edge of Marx Brothers humor, which later became a heavy influence on Bugs Bunny cartoons.
One direct example of that influence occurs in the speakeasy. Two men are playing cards, and one says to the other, "cut the cards". Pinky happens to walk by at that moment, pulls a large meat cleaver out of his trenchcoat and chops the deck in half. This none-too-subtle gag, which was recycled from the brothers' first Broadway show, I'll Say She Is, would be repeated by Curly Howard against Moe Howard in the Three Stooges' 1936 short subject Ants in the Pantry, and by Bugs Bunny against Yosemite Sam in the 1948 cartoon, Bugs Bunny Rides Again.
During the climactic football game, at one point Groucho utters the exclamation, "Jumping anaconda!" This seemingly nonsensical phrase probably is a reference to the notorious stock market performance of Anaconda Copper immediately preceding the Great Depression. Groucho had delivered other jokes related to the stock market in the Brothers' preceding films (for example, "The stockholder of yesteryear is the stowaway of today" in Monkey Business) and all the Marx Brothers had experienced severe losses in the 1929 crash.