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.
Dimentio in the third game. Including Super Dimentio.
Complacent Gaming Syndrome: The only thing anyone ever levels up is BP. They even pay an NPC to relocate the extra 5 HP you start with (you start with 10) to BP so that Mario is permanently in the Danger state and can always reap the rewards of many badges that take effect in this state. These badges do things like increase Mario's attack and defence, and even make enemies miss sometimes, and they stack, so you make Mario able to do tons of damage and take absolutely none, effectively turning on god mode. This is known as the "Danger Mario" build.
Ensemble Darkhorse: Holy cow. Every game has a lot of characters that became fan favorites. Paper Mario has Bombette, Kammy, the Koopa Bros, and the Crystal King. The Thousand-Year Door has Goombella, Admiral Bobbery, Vivian, Cortez, Rawk Hawk, Doopliss, and Lord Crump. Super Paper Mario has the entire villain team (Count Bleck, Dimentio, Mimi, O'Chunks, Nastasia and Mr. L).
Fridge Horror: In the first game, everyone in the castle is lifted up into the sky, save for Luigi and a few toads (who escaped.) When you explore it as Peach, and later, Mario, it's almost completely empty. What exactly happened to them?
Nothing... Well, except getting thrown into a cell. A little while after getting to Bowser's Castle, you can get to a cell where you'll find the guests and guards from the beginning of the game. At least, the ones that couldn't get away in time.
Mario might have just not found all the cells. If that's the case, we could probably just assume that they'd just go find them some other time.
Fridge Logic: A hilarious (and very fortunate) in-universe example. Right when Mario leaves Lavalava Island, Jr. Troopa shows up, having swam all the way there. He misses Mario and has to swim all the way BACK to Toad Town. When Mario fights Jr. Troopa at Toad Town Harbor, his HP will be halved at the start of the battle. After Mario beats him, Jr. Troopa will realize he could've just flown to Lavalava Island and back since he has wings.
The Dotwood Tree in Super Paper Mario. If you get hit by a Crayzee Dayzee mid-jump (and this is a very jumpcentric level), which you probably will, you'll probably end up falling a good distance and having to do large chunks of the level over again.
The Scrappy: Twink in the first game, for generally being annoying.
Woobie: Shadow Siren Vivian is often wrongfully and mercilessly disciplined by her sister Beldam. If you feel like treating her right, well, Chapter 4 seems like the right time to start because Doopliss steals Mario's body and Vivian's sisters leave her alone while they slack off. She will join you after you console her, but eventually, she'll find out who consoled her, but she'll stay.