The ending of "Doug Gets His Ears Lowered", where Roger tries to chase off some squirrels who are laughing at the silly haircut "Fluke" gave him.
Doug trying to seduce his teacher as Smash Adams. "I was just noticing what... large, hair you have!"
Also from that episode, Doug's premature confession which lead to Mrs. Wingo saying:
Mrs. Wingo: You wrote a paper titled My First Pair Of High Heels?"
Nearly everything we've seen of Judy's art school, Moody School. In some of its art labs we've seen a guy chopping a car in half with a guillotine, a musician playing a watermelon slice like a violin, two opera singers singing in a room filled with water without oxygen gear, and a guy just floating in the air.
Doug imagining getting chased by a pot roast when he imagines what the bone he found may've been.
"In other news, Mr. Bone wears pink underwear."
Doug's nervous about Judy performing at his school. In a daydream, Judy pulls out Doug's underwear and tosses it onto his head, causing the entire auditorium to erupt in hysterical laughter.
In the episode Doug Didn't Do It, Doug is framed by Roger for stealing a trophy from Mr. Bone and as punishment has to polish 305 trophies. While Doug waits in Mr. Bone's office, Roger then sneaks in and proceeds to do some Evil Gloating. Only thing is, he accidentally turns on the school PA and his confession is heard throughout the entire school. And when Mr. Bone angrily bursts into the office to confront him, Roger lets out a high-pitched scream.
Mrs. Wingo is reading to the class: "And then, King Ludwig of Bavaria went insane." One of the most out-of-context lines ever.
In "Nightmare on Jumbo Street", one of Doug's nightmares involves Porkchop impersonating Jack Nicholson for some reason.