Politically Motivated Teacher: Played positively, and seen entirely outside of the classroom, too. Kate fiercely opposes racism against Monsters, and her biggest dream is to someday open up a Monsters-only school.
Laser-Guided Karma: After being the Spanner in the Works (see below) she ends up being hit by the penny Kate drops off the Empire State Building and put in the hospital, eventually dying (temporarily). Lampshaded by Kate, who first feels horrible for having dropped the penny, then once she realizes Lucy's spanner role: "I feel better now."
Innocently Insensitive: When Rod talks to her about his friend who's gay, she says there's nothing wrong with it until Rod says the friend is also a conservative at which point she says they should just stay in the closet.
Japanese Ranguage: Not extremely, but it's always there. Don't worry, though; Everyone's A Rittle Bit Lacist.
The Obi-Wan: For Kate Monster, when it comes to relationship advice.
Butt Monkey: Very much. The song "It Sucks to be Me," the characters sing about how their lives are so much worse than everyone else's . . . until Gary pops in. Then everyone cheerfully agrees that he wins the Misery Poker.