Constant iffy behavior and several iffy messages, particularly around the idea of masculinity; the movie seems to regard getting in the fight as a mark of maturity and courage. Authority figures are thoughtless and don't care about the students they're responsible for.
Violence, while played for laughs, is surprisingly brutal. A teacher throws objects around his classroom and destroys a student's desk with an axe. He also threatens another man many times. The "fist fight" of the title is long and merciless: Characters throw each other into metal and glass (breaking a windshield), one character hits another in the head with a fire extinguisher, and both are knocked unconscious, one multiple times. Despite all this, no one is seriously injured (even though the head-knocks look like they could cause brain damage). In a brief scene, torture is implied, and a (fantasy) character is shot in the head with blood but no gore. Bullying.
Brief glimpse of footage from a porn movie shows two women pressing their naked breasts together. A guidance counselor jokes frequently about finding the teen students at her school attractive; she leers at the teens and calls them "fine" (at the end of the movie, it's implied that a graduating student returns her affections and that it's OK for them to get together because he's "not a student anymore"). Running joke about a student masturbating in a bathroom stall; no private parts are visible. A sign (promoting vegetarianism?) tells students to "Eat p---y, not meat."
Very frequent swearing, including "s--t," "f--k," "ass," "hell," "damn," "bulls--t," "motherf---ker," "d--k," "boner," "balls," "a--hole," "son of a b---h," "goddamn." A man is called a "b--h" and a "p----y" many times when characters are goading him into a fight, implying he's not masculine. A sign instructs students to "Eat p---y, not meat."
Characters visit an Apple store twice and talk about wanting a Mac and an iPhone; the features of the laptop are discussed excitedly by characters. Apple logos are visible on every cell phone.
A teacher jokes about buying and using meth. Students feed a horse meth to get it to run through school halls. A plot point revolves around a teacher planting drugs ("Molly") on another to get him arrested. Students and teachers alike smoke marijuana at school. A teacher's drug habit is played for laughs.