Billy supposedly touches the teacher's breast (but it doesn't really look like he does) because of a double dare.
The goofy bus driver looks up a woman's skirt, as she walks up the school bus stairs, and presumably sees her underwear.
In a fantasy sequence, a woman says to a man "Don't I have a great rack?"
A man is wiping a naked (looks like a man) statue's butt, with a cloth, while he has a book in his other hand. This lasts for 4 or 5 seconds.
On another scene, Billy finally gets the question right, but it's his (male) bus driver that takes his shirt off.
Billy Madison draws a picture with bare breasts this scene is over shortly but played long enough to understand what it is.
On Valentine's day billy gets several letters in class one of them is from the (male) principal and at the bottom the card says "im horny"
Billy is studying for a test, and his teacher takes off one piece of clothing for a correct answer. Billy gets a history question wrong, so the teacher is fully dressed when she decides to leave.
Billy kisses a photograph (of a woman he really likes at school), he moves his hand in a cup-shape form underneath the photograph.
Billy and Teacher kiss, Billy fondling her butt. Two of Billy's friends gives him a thumbs up.
A man says he wants to touch a woman's "hiney".
At the end of the movie, after Billy's speech, people are kissing one another, the bus driver kisses a human-sized penguin and licks its beak and puts the end of it in his mouth. The Penguin lowers his flippers in a lower motion, as the bus driver makes faces in a sexual way.