These are what we call the 'YMMV items.' Things that some people find in this work. We call them 'your mileage might vary' because not everyone sees these things in the same way. This starts discussions in the trope lists, a thing we don't want. Please use the discussion page if you'd like to discuss any of these items.
Big Lipped Alligator Moment: Too many to count, basically the writers are adding too many jokes for the episodes that it's almost hard to pay attention to the show itself.
Fridge Brilliance: Why does the theme song in the episode Mr. Kidd replace Adam with Mr. Kidd ? Because the episodes plot revolves around Kidd trying to whipe Adam out of everyone's memories and replacing him.
Also in "Mr. Kidd", Derby is surprised to hear that Adam's a science teacher. While not intelligent, Derby is usually not that stupid-unless Mr. Kidd had already tested out the Reversed Memory-Eraser on him beforehand.
In "Mr. Switch", Adam, Echo, Slabb, Ivy, Derby, and Dang accidentally switch bodies, and trade clothing in order to make it easier to remember who's who. Adam as Echo comes up with the excuse that it's "Dress-As-Your-Favourite-Person-Day". If this were true, Echo's favourite person would be Adam, and Ivy's would be Slabb. Hence Foreshadowing both of the later Official Couples.
Derby tells Adam in "Mr. First Impression", Derby tells Adam that first impressions are everything. He's talking about it in terms of relationships, but it could also apply to his character. Several episodes, mostly early on, show Derby as actually being quite clever when he's actually motivated, but nothing important ever comes of it and the characters never think of him as anything other than a complete idiot (except in "Mr. Switch", but only because Derby was actually Echo) because that's how he was introduced in the first episode.
Also in "Mr. First Impression", why, in one timeline, does Mrs. Byrne teach about the war between the humans and the elephants? Because Adam went back in time and prevented the War of 1812, so she needed something new to define her identity.
Hilarious in Hindsight: Adam and Derby mocking the idea of Tater having a son in "Mr. Brain" becomes even funnier in "Mr. Kidd" when it's revealed that Tater had sexual relations with Rachel and might actually be Adam's father.
Ho Yay: In "Mr. Meteor", Slabb tells Adam "I wonder what our kids are gonna look like!" (He was actually talking about starting a petting zoo with baby goats, but still).
In "Mr. Student", Derby comforts a girl after Hutch breaks up with her, which causes him to think she has a crush on her. The episode ends with Derby doing the same thing to Hutch that he did to the girl in the beginning, word-for-word, after Ivy breaks up with Hutch.
Mary Sue: Echo seems to be a parody of this trope.
Fixer Sue: Dang also seems to be a parody of this one.
Moral Event Horizon: The title character in Mr. Kidd tries to take Adam's place as a teacher. Not bad enough? Okay, how about wiping everyone's memory of Adam, including his mother? No good reason was given for this so it's definitely For the Evulz.
Nightmare Fuel: The fact that the CEO of Cyclops Industries is a REAL Cyclops.
In his return episode, Mr. Cyclops buys out the school to work on his products and has the cafateria sell only the food made by his corperation, which temporarily mutates everyone into Cyclopses.
Mr. Kidd, the guy tries to steal Adam's life by eraseing everyone's memories of him - his friends, girlfriend, family, and co workers.
The subplot of Mr. Interview which virtually shatters the fourth wall.
Suspiciously Similar Song: The Kiss Cam theme sounds similar to "Kiss Me." "Derby Style" is a more obvious pastiche of "Gangnam Style." "There Is A Perfect School I Know" is one to "Castle On A Cloud".