Crocodile Tears: Weaponised by Bart and Lisa to skip the line for a waterside. Lisa starts crying and screaming "I want my mommy!" while Bart acts like the concerned big brother, pushing past everyone with Lisa close behind.
Determinator: Ringo Starr is determined to personally answer each and every piece of fan mail he's ever gotten, which is why it took so long for him to answer Marge about her portrait of him.
Didn't Think This Through: Homer gets stuck in the H2WHOA! slide, and one of the lifeguards decides to send more kids down to dislodge the blockage, thinking it's too big to be human. This makes the problem worse because the kids end up crashing into Homer and the part of the slide with him stuck in it has to be removed in order to get him out.
Diet Episode: The first for Homer. Played more realistically than most in that Homer's weight loss isn't dramatic or significant enough to alter his appearance much, he simply loses enough to reach a healthier weight (and because he was humiliated on the news).
Early Installment Weirdness: Somewhat minor; Homer caring deeply about his weight is something that would certainly never happen in later seasons, given how gluttonous and care-free he is when it comes to food and beer. While he has gotten into shape in later episodes, he loses it by the next episode. In the case of "Kamp Krusty," Homer gains the weight back at once when he finds out what Bart had done to the camp.
Also minor is Lisa willingly helping Bart in committing mischief - specifically, joining him in chanting "Can we go to Mount Splashmore" to pester Homer and pretending to be a lost girl to get first in line for a ride - when in later seasons she would have nothing to do with Bart's antics.
Jerk with a Heart of Jerk: Marge discovers that Mr. Burns has absolutely no redeeming qualities, making it difficult for her to make a good painting of him. She tries to tell him she can't paint a positive picture of him due to his behavior, but Mr. Burns cuts her off by saying he needs the painting done on time and tells her to shut up and paint.
Kent Brockman News: The news anchors cracking jokes about Homer's weight while on the air.
Kick the Dog: Burns making fun of Homer's attempt at losing weight, driving Homer to binge on food again until Marge stops him. It is also the final straw to Marge realizing Burns has no redeeming qualities and pretty much tells him to get out.
Moral Event Horizon: In-universe. Mr. Burns crosses this in Marge's eyes with the aforementioned remark about Homer's weight. Marge even lampshades it.
Marge: I used to think there was good in everyone until I met that man!
No Name Given: Subverted. Apu's first name is revealed in this episode.
Out-of-Character Moment: Lisa pretending to cry so that she and Bart and move to the front of the line. It's one of the few times she's shown to willingly join in one of Bart's scams.
Rousing Speech: Homer gives one to himself, resolving to go through with his diet.
Homer: I'm going on a diet. From now on, there'll be no pork chop too succulent, no donut too tasty, no pizza too laden with delicious toppings to prevent me from reaching my ideal weight! As God as my witness, I'll always be hungry again! (stomach growls) D'oh! Shut up.
Scenery Censor: Marge runs into Mr. Burns getting out of the shower, his private parts covered up by her arm. Later, when Marge's portrait of Burns is unveiled and it turns out to be nude, the crotch keeps being blocked by people's heads or hands.